tag:blogger.com,1999:blog-7747384495945159272011-12-16T05:46:10.853-08:00LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.comBlogger681100tag:blogger.com,1999:blog-774738449594515927.post-30548745732123487982009-03-25T09:50:00.000-07:002009-03-26T07:33:03.554-07:00we don't have time to post the whole solution but this problem need to be solved using differential equation to get the exact answer... we probably post during the weekend...<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-3054874573212348798?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com14tag:blogger.com,1999:blog-774738449594515927.post-28916609706668197962009-03-22T15:00:00.000-07:002009-03-22T17:12:48.776-07:00Today, we have decided to revive the blog. We are still busy with school and work. However, we still want to have some fun and archive old puzzles.<br /><br />However, we do not guarantee to post solutions at the time of the puzzle. Instead, we create an empty page and allow discussing through comments for each puzzle (Thanks to the advance posting feature from Blogger). We will post solutions when we have free time (mostly during weekend).<br /><br />In this way, some people can't complain that they can't get into first 250 because of our site. However, we still provide solutions/hints for those who struggle. So I hope everyone will be happy.<br /><br />LC Solver<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-2891660970666819796?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-2859092178364238122009-03-19T16:45:00.000-07:002009-03-25T09:50:31.946-07:00Date Released: March 19th, 2009.<br />Date Rewarded: March 26th, 2009. (estimated)<br /><p>Rearrange the letters in the following phrase to come up with a Neopian word or phrase:</p> <p style="text-align: center;"><b><i>ROTATE SOON VIA RAIL</i></b></p> <p>Submit only the answer with no other information, otherwise your answer will be marked as incorrect!</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><img src="http://images.neopets.com/items/can_train_gummy.gif" /><br /><u>Steam Train Gummies</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution303')"><u>Click to show/hide hint</u></a><br /><div class="commenthidden" id="Solution303">It is related to a character in the current Daily Dare event: <span style="font-weight: bold;">Aristotle A Avinroo</span>.<br /></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-285909217836423812?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com1tag:blogger.com,1999:blog-774738449594515927.post-79342305504108711262009-03-12T17:39:00.000-07:002009-03-22T18:56:57.409-07:00Date Released: March 12th, 2009.<br />Date Rewarded: March 17th, 2009.<br /><p style="text-align: center;">271 - 482 = 436 </p><p style="text-align: center;">148 + 591 = 866 </p><p style="text-align: center;">4881 + 8914 = 6562 </p><p style="text-align: center;"><b>8827 * 1178 = ?</b></p> <p>Do NOT show your work; submit only a single number, with no punctuation, as your answer.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/petpet_robo_wheel.gif" /><br /><u>Rotawheel</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution302')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution302"><br /><p>To be easy to work on this problem, we convert all the digits into alphabetical letters in the following scheme: <span style="font-style: italic;">a</span> = 1, <span style="font-style: italic;">b</span> = 2, <span style="font-style: italic;">c</span> = 3, <span style="font-style: italic;">d</span> = 4, <span style="font-style: italic;">e</span> = 5, <span style="font-style: italic;">f</span> = 6, <span style="font-style: italic;">g</span> = 7, <span style="font-style: italic;">h</span> = 8, <span style="font-style: italic;">i</span> = 9. Then we have three equations:</p><p style="text-align: center;"><span style="font-style: italic;">bga</span> = <span style="font-style: italic;">dhb</span> + <span style="font-style: italic;">dcf</span> (1)<br /><span style="font-style: italic;">adh</span> + <span style="font-style: italic;">eia</span> = <span style="font-style: italic;">hff</span> (2)<br /><span style="font-style: italic;">dhha</span> + <span style="font-style: italic;">hiad</span> = <span style="font-style: italic;">fefb</span> (3)<br /></p><p>Before we solve the problem, we have to assume that each letter represent a unique digit (distinct property.) For example, if <span style="font-style: italic;">a</span> is 4, then <span style="font-style: italic;">b</span> must <span style="font-weight: bold;">not</span> be 4. Also, all the digits in the hundreds' places in (1) and (2) and thousands' places in (3) must <span style="font-weight: bold;">not</span> be 0.<br /><br />If we look at the equation (1) at the hundreds' place, we have <span style="font-style: italic;">b</span> = <span style="font-style: italic;">d</span> + <span style="font-style: italic;">d</span>. So, we know that 1 <= d <= 4 because <span style="font-style: italic;">d</span> can't be 0 and if <span style="font-style: italic;">d</span> >= 5 then <span style="font-style: italic;">b</span> is not a digit. There are four cases:</p><ul><li><span style="font-style: italic;">d</span> = 1: <span style="font-style: italic;">b</span> can be either 2 or 3 (in the case of carry from the tens' place.)</li><li><span style="font-style: italic;">d</span> = 2: <span style="font-style: italic;">b</span> can be either 4 or 5.</li><li><span style="font-style: italic;">d</span> = 3: <span style="font-style: italic;">b</span> can be either 6 or 7.</li><li><span style="font-style: italic;">d</span> = 4: <span style="font-style: italic;">b</span> can be either 8 or 9.</li></ul><br />If we look at the equation (3) at the unit's place, we have <span style="font-style: italic;">a</span> + <span style="font-style: italic;">d</span> = <span style="font-style: italic;">b</span>. Then, the four cases will be following:<p></p><ul><li><span style="font-style: italic;">d</span> = <span style="font-weight: bold;">1</span>: <strike><span style="font-style: italic;">b</span> = 2 => <span style="font-style: italic;">a</span> = <span style="font-weight: bold;">1</span></strike> (violate the distinct property), <span style="font-style: italic;">b</span> = 3 => <span style="font-style: italic;">a</span> = 2<br /></li><li><span style="font-style: italic;">d</span> = <span style="font-weight: bold;">2</span>: <strike><span style="font-style: italic;">b</span> = 4 => <span style="font-style: italic;">a</span> = <span style="font-weight: bold;">2</span></strike> (violate the distinct property), <span style="font-style: italic;">b</span> = 5 => <span style="font-style: italic;">a</span> = 3</li><li><span style="font-style: italic;">d</span> = <span style="font-weight: bold;">3</span>: <strike><span style="font-style: italic;">b</span> = 6 => <span style="font-style: italic;">a</span> = <span style="font-weight: bold;">3</span></strike> (violate the distinct property), <span style="font-style: italic;">b</span> = 7 => <span style="font-style: italic;">a</span> = 4</li><li><span style="font-style: italic;">d</span> = <span style="font-weight: bold;">4</span>: <strike><span style="font-style: italic;">b</span> = 8 => <span style="font-style: italic;">a</span> = <span style="font-weight: bold;">4</span></strike> (violate the distinct property), <span style="font-style: italic;">b</span> = 9 => <span style="font-style: italic;">a</span> = 5</li></ul><br />If we look at the equation (1) at the unit's place, we have <span style="font-style: italic;">a</span> = <span style="font-style: italic;">b</span> + <span style="font-style: italic;">f</span>. Then, the four cases will be following:<br /><ul><li><span style="font-style: italic;">d</span> = 1: <span style="font-style: italic;">a</span> = 2, <span style="font-style: italic;">b</span> = 3 => <span style="font-style: italic;">f</span> = 9</li><li><span style="font-style: italic;">d</span> = 2: <span style="font-style: italic;">a</span> = 3, <span style="font-style: italic;">b</span> = 5 => <span style="font-style: italic;">f</span> = 8</li><li><strike><span style="font-style: italic;">d</span> = 3: <span style="font-style: italic;">a</span> = 4, <span style="font-style: italic;">b</span> = <span style="font-weight: bold;">7</span> => <span style="font-style: italic;">f</span> = <span style="font-weight: bold;">7</span></strike> (violate the distinct property)</li><li><span style="font-style: italic;">d</span> = 4: <span style="font-style: italic;">a</span> = 5, <span style="font-style: italic;">b</span> = 9 => <span style="font-style: italic;">f</span> = 6</li></ul><br />There are only three cases left after the last analysis. If we look at the equation (2) at the unit's place, we have <span style="font-style: italic;">h</span> + <span style="font-style: italic;">a</span> = <span style="font-style: italic;">f</span>. Then, the three cases will be following:<br /><ul><li><span style="font-style: italic;">d</span> = 1: <span style="font-style: italic;">b</span> = 3, <span style="font-style: italic;">f</span> = 9, <span style="font-style: italic;">a</span> = 2 => <span style="font-style: italic;">h</span> = 7<br /></li><li><strike><span style="font-style: italic;">d</span> = 2: <span style="font-style: italic;">b</span> = <span style="font-weight: bold;">5</span>, <span style="font-style: italic;">f</span> = 8, <span style="font-style: italic;">a</span> = 3 => <span style="font-style: italic;">h</span> = <span style="font-weight: bold;">5</span></strike> (violate the distinct property)</li><li><span style="font-style: italic;">d</span> = 4: <span style="font-style: italic;">b</span> = 9, <span style="font-style: italic;">f</span> = 6, <span style="font-style: italic;">a</span> = 5 => <span style="font-style: italic;">h</span> = 1</li></ul><br />There are only two cases left now. However, if we look at the equation (2) at the hundreds' place, we have <span style="font-style: italic;">a</span> + <span style="font-style: italic;">e</span> = <span style="font-style: italic;">h</span>. In the last case, <span style="font-style: italic;">a</span> = 5 and <span style="font-style: italic;">h</span> = 1. It is impossible to get since <span style="font-style: italic;">h</span> > <span style="font-style: italic;">a</span>. Therefore, only the first case is correct. Then, we have: <span style="font-style: italic;">a</span> = 2, <span style="font-style: italic;">b</span> = 3, <span style="font-style: italic;">d</span> = 1, <span style="font-style: italic;">f</span> = 9, <span style="font-style: italic;">h</span> = 7<br /><br />Now, we look at the equation (2) at the tens' place. Since there is no carry on the unit's place addition, we can write: <span style="font-style: italic;">d</span> + <span style="font-style: italic;">i</span> = <span style="font-style: italic;">f</span> <=> <span style="font-style: italic;">i</span> = <span style="font-style: italic;">f</span> - <span style="font-style: italic;">d</span> = 9 - 1 = 8 (no carry either). Then, we look at the same equation at the hundreds' place, we can write: <span style="font-style: italic;">a</span> + <span style="font-style: italic;">e</span> = <span style="font-style: italic;">h</span> <=> <span style="font-style: italic;">e</span> = <span style="font-style: italic;">h</span> - a = 7 - 2 = 5.<br /><br />Then, we look at the equation (1) at the tens' place. Since there is a carry on the unit's place (<span style="font-style: italic;">a</span> = 2 = 3 + 9 = <span style="font-style: italic;">b</span> + <span style="font-style: italic;">f</span>), we can write: <span style="font-style: italic;">g</span> = <span style="font-style: italic;">h</span> + <span style="font-style: italic;">c</span> + 1 <=> <span style="font-style: italic;">g</span> = <span style="font-style: italic;">c</span> + 8. Since 1, 2, 3, 5, 7, 8, 9 are already taken. <span style="font-style: italic;">c</span> and <span style="font-style: italic;">g</span> can only be 0, 4 or 6. Only the pair <span style="font-style: italic;">c</span> = 6 and <span style="font-style: italic;">g</span> = 4 are satisfied this equation. Therefore, we have: <span style="font-style: italic;">a</span> = 2, <span style="font-style: italic;">b</span> = 3, <span style="font-style: italic;">c</span> = 6, <span style="font-style: italic;">d</span> = 1, <span style="font-style: italic;">e</span> = 5, <span style="font-style: italic;">f</span> = 9, <span style="font-style: italic;">g</span> = 4, <span style="font-style: italic;">h</span> = 7, <span style="font-style: italic;">i</span> = 8.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-7934230550410871126?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-38413382995664405182009-03-04T18:45:00.000-08:002009-03-04T18:46:59.370-08:00I should be back here soon but can't spend too much time on it now... We will do a survey to see what answer you submitted last week. It may not be accurate but it's worth a shot...<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-3841338299566440518?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com12tag:blogger.com,1999:blog-774738449594515927.post-51646323624961184222008-12-31T08:54:00.000-08:002008-12-31T08:55:34.672-08:00I'm not online New Year Eve. If this round comes out soon, feel free to discuss. I will update later. Happy New Year :)<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-5164632362496118422?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com64tag:blogger.com,1999:blog-774738449594515927.post-90160803049093906672008-12-17T15:19:00.000-08:002008-12-17T15:23:13.992-08:00Check the Hidden Tower<br /><a href="http://www.neopets.com/faerieland/hiddentower938.phtml"><br />http://www.neopets.com/faerieland/hiddentower938.phtml</a><br /><br />Use the second letter of each item to get the question and check the Hidden Tower for the answer. Good luck!<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-9016080304909390667?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com17tag:blogger.com,1999:blog-774738449594515927.post-25889098392535983402008-12-10T18:09:00.001-08:002009-03-22T18:46:53.155-07:00Thanks for all the comments. Look like it is a good answer<br /><br />Advent Calendar <a href="http://www.neopets.com/%7Eloveywovey#08">NP rewards</a>:<br /><br />Day 1: 324 NPs<br />Day 2: 945 NPs<br />Day 3: 394 NPs<br />Total: 324 + 945 + 394 = 1663 NPs<br /><br />Day 4: 295 NPs<br />Day 5: 953 NPs<br />Day 6: 279 NPs<br />Total: 295 + 953 + 279 = 1527 NPs<br /><br />Day 7: 273 NPs<br />Day 8: 479 NPs<br />Day 9: 374 NPs<br />Total: 273 + 479 + 374 = 1126 NPs<br /><br />Day 10: 179 NPs<br />Day 11: 278 NPs<br />Day 12: 639 NPs<br />Total: 179 + 278 + 639 = 1096 NPs<br /><br />Day 13: 730 NPs<br />Day 14: 579 NPs<br />Day 15: ? NPs<br />Total: 730 + 579 + ? = 1309 + ? = ? NPs<br /><br />Good luck :)<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-2588909839253598340?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com40tag:blogger.com,1999:blog-774738449594515927.post-48824863035217067882008-11-26T18:31:00.000-08:002008-12-03T17:19:21.967-08:00Crosses all the worlds, we get the below:<br /><br /><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 400px; height: 366px;" src="http://2.bp.blogspot.com/_I-kT7eLPpXY/STcuBaHfxWI/AAAAAAAAAJ8/8suDkPgnFhU/s400/round_289.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5275736090213336418" /><br /><br /><br />The question is read backwards from the remaining letters:<br /><br />"what is the numeric deactivation code for the evil program dr sloth created?"<br /><br />Check step 24 of the below link<br /><br /><a href="http://www.neopets.com/space/npv2_solution.phtml">http://www.neopets.com/space/npv2_solution.phtml</a><br /><br />(Please submit the answer with no <span style="font-weight:bold;">spaces</span> or punctuation)<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-4882486303521706788?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com34tag:blogger.com,1999:blog-774738449594515927.post-690258535618644912008-11-19T15:31:00.000-08:002008-11-19T15:33:42.107-08:00Ra<br />Shah<br />Roo<br />Ee<br /><a href="http://www.neopets.com/pronounce.phtml"><br />http://www.neopets.com/pronounce.phtml</a><br /><br />check out the first four pets then you know the next one... :)<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-69025853561864491?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com13tag:blogger.com,1999:blog-774738449594515927.post-80077709869035192622008-11-12T16:32:00.001-08:002008-11-12T20:49:06.229-08:00I think this may be the final version.<br /><br />Tier 1: r1 = d1/2 = 6 in (bottom)<br />Tier 2: r2 = d2/2 = 5.25 in (middle)<br />Tier 3: r3 = d3/2 = 4.5 in (top)<br />Height: h = 1.5 in (height of a layer)<br /><br />V(cake) = pi * ((r1-1/3)^2 + (r2-1/3)^2 + (r3-1/3)^2) * (3*h)<br /><br />V(frost_side) = pi * (2/3 r1 + 2/3 r2 + 2/3 r3 - 1/3) * (3*h+1/2)<br />V(frost_top) = pi * (r1^2 + r2^2 + r3^2) * 1/3<br />V(frost) = V(frost_top) + V(frost_side)<br /><br />V(jam) = pi * ((r1 - 1/3)^2 + (r2 - 1/3)^2 + (r3 - 1/3)^2) * 1/2<br /><br />weight = V(cake) * 0.35 + V(frost) * 0.48 + V(jam) * 0.6<br /><br />cal = weight * 53.4<br /><br />Remember not to round before the the final answer. Good luck.<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-8007770986903519262?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com38tag:blogger.com,1999:blog-774738449594515927.post-64038742124619378812008-11-05T18:19:00.001-08:002008-11-05T18:23:00.379-08:00This is a guessing game again. I think the answer could be one of those with high points: Chomby (39), Mynci (35), Xweetok (31), Scorchio (25), Usul (23), Eyrie (22), Ogrin (20), Peophin (20), Blumaroo (19), Nimmo (19), Poogle (19)<br /><br />Your choice of submission<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-6403874212461937881?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com22tag:blogger.com,1999:blog-774738449594515927.post-47824084627613883432008-10-29T14:57:00.000-07:002008-10-29T17:38:58.088-07:00This is the total points for each Neopet. Look like they are matched with the comments (at least one of them)<br /><br /><br />Acara: 7<br />Aisha: 7<br />Blumaroo: 19<br />Bori: 12<br />Bruce: 7<br />Buzz: 10<br />Chia: 13<br />Chomby: 39<br />Cybunny: 11<br />Draik: 55<br />Elephante: 42<br />Eyrie: 22<br />Flotsam: 8<br />Gelert: 18<br />Gnorbu: 8<br />Grarrl: 9<br />Grundo: 9<br />Hissi: -1<br />Ixi: 21<br />Jetsam: 5<br />JubJub: 12<br />Kacheek: 15<br />Kau: 5<br />Kiko: 13<br />Korbat: 9<br />Kougra: 7<br />Krawk: 6<br />Kyrii: -2<br />Lenny: 9<br />Lupe: 11<br />Lutari: 3<br />Meerca: 15<br />Moehog: 13<br />Mynci: 35<br />Nimmo: 19<br />Orgin: 20<br />Peophin: 20<br />Poogle: 19<br />Pteri: 3<br />Quiggle: 18<br />Ruki: 8<br />Scorchio: 25<br />Shoyru: 10<br />Skeith: 12<br />Techo: 13<br />Tonu: 13<br />Tuskanniny: 26<br />Uni: 13<br />Usul: 23 <br />Wocky: 11<br />Xweetok: 31<br />Yurble: 13<br />Zafara: 1<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-4782408462761388343?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com78tag:blogger.com,1999:blog-774738449594515927.post-62335443096955374812008-10-22T16:40:00.001-07:002008-10-22T17:09:17.619-07:00Use the base converter below for conversion<br /><br /><a href="http://www.mste.uiuc.edu/users/exner/ncsa/base/">http://www.mste.uiuc.edu/users/exner/ncsa/base/</a><br /><br />I found that the following is match:<br />553 (base 13)<br />546 (base 23)<br />897 (base 17)<br />318 (base 19)<br /><br />converts all 4 numbers into base 10 and sum them up then convert back to the base 32 and submit the answer.<br /><br />This is where you can learn about base:<br /><a href="http://en.wikipedia.org/wiki/Base_(mathematics)">http://en.wikipedia.org/wiki/Base_(mathematics)</a><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-6233544309695537481?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com34tag:blogger.com,1999:blog-774738449594515927.post-89292561745996241202008-10-15T17:36:00.001-07:002008-10-15T19:35:03.155-07:00What do you get when you multiply six by nine?<br /><br />If there is no tricks, you shouldn't need hints? or would you... ?<br /><br />Some people suggest this one:<br /><a href=" http://en.wikipedia.org/wiki/Answer_to_life_the_universe_and_everything#Arthur.27s_Scrabble_tiles"><br />http://en.wikipedia.org/wiki/Answer_to_life_the_universe_and_everything#Arthur.27s_Scrabble_tiles</a><br /><br />Logically, I don't really see the reason for it but feel free to answer what you like. Maybe it is the answer.... We never know...<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-8929256174599624120?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com36tag:blogger.com,1999:blog-774738449594515927.post-7626762030674300742008-10-09T17:05:00.000-07:002008-10-08T21:28:33.058-07:00Date Released: October 9th, 2008.<br />Date Rewarded: October 16th, 2008.<br /><br />As you may know, each Neopets item has a numerical rarity associated with it. So add up the following: <p>The rarity of the item awarded in Lenny Conundrum #92<br />+ The rarity of the item awarded in Lenny Conundrum #107<br />+ The rarity of the item awarded in Lenny Conundrum #129<br />+ The rarity of the item awarded in Lenny Conundrum #142<br />+ The rarity of the item awarded in Lenny Conundrum #192<br />+ The rarity of the item awarded in Lenny Conundrum #219<br />+ The rarity of the item awarded in Lenny Conundrum #229<br />+ The rarity of the item awarded in Lenny Conundrum #281 </p> <p><b>What is the total?</b> If a rarity has changed since the prize was first awarded, go with the <i>current</i> rarity. And please, submit only a number with no punctuation or other information.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/fur_autumn_leaf_wreath.gif" /><br /><u>Autumn Leaf Wreath</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution282')"><u>Click to show/hide hints</u></a><br /><div class="commenthidden" id="Solution282"><br />The prize for each round and its rarity are below:<br /><br />Round 92 - Happy Birthday Negg (rarity 89)<br />Round 107 - Filamen (rarity 89)<br />Round 129 - Ice Scimitar (rarity 87)<br />Round 142 - Baby Rattle (rarity 92)<br />Round 192 - Large Chia Cake (rarity 90)<br />Round 219 - Wartroot Snorkle Lollypop (rarity 82)<br />Round 229 - Quill and Ink (rarity 91)<br /><a href="http://lennyconundrumsolutions.blogspot.com/2008/10/round-281.html">Round 281</a> - Grandfather clock (rarity 90)<br /><br />Note: Brain Tree Mace is not a correct prize for round 107.<br /><br />The answer is the sum of all rarity numbers.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-762676203067430074?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com73tag:blogger.com,1999:blog-774738449594515927.post-60080126349422006802008-10-02T19:17:00.000-07:002008-10-09T21:17:59.218-07:00Date Released: October 2nd, 2008.<br />Date Rewarded: October 9th, 2008.<br /><p>Walking into <a href="http://www.neopets.com/objects.phtml?type=shop&amp;obj_type=104">Chesterdrawer's Antiques</a>, you notice several clocks on the wall. The first clock reads 9:00, the second reads 6:07, the third 10:45, the fifth 7:45, the sixth 7:52, and the seventh 4:37.</p> <p><b>What should the fourth clock read?</b></p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/nfu_neovia_clock.gif" /><br /><u>Grandfather Clock</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution281')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution281"><br />First we convert the clock time into position of hour and minute hands of 12 hour dial face. Then, we use the Flag Semaphore Character chart [1] to decode the hands.<br /><br /><div style="text-align: center;"><table align="center" border="1"><tbody align="center"><tr><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/35/Semaphore_Alpha.svg/60px-Semaphore_Alpha.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Semaphore_Bravo.svg/60px-Semaphore_Bravo.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Semaphore_Charlie.svg/60px-Semaphore_Charlie.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Semaphore_Delta.svg/60px-Semaphore_Delta.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Semaphore_Echo.svg/60px-Semaphore_Echo.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/33/Semaphore_Foxtrot.svg/60px-Semaphore_Foxtrot.svg.png" /></td></tr><tr><td>A</td><td>B</td><td>C</td><td>D</td><td>E</td><td>F</td></tr><tr><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/0/01/Semaphore_Golf.svg/60px-Semaphore_Golf.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Semaphore_Hotel.svg/60px-Semaphore_Hotel.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Semaphore_India.svg/60px-Semaphore_India.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/13/Semaphore_Juliet.svg/60px-Semaphore_Juliet.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Semaphore_Kilo.svg/60px-Semaphore_Kilo.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Semaphore_Lima.svg/60px-Semaphore_Lima.svg.png" /></td></tr><tr><td>G</td><td>H</td><td>I</td><td>J</td><td>K</td><td>L</td></tr><tr><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/39/Semaphore_Mike.svg/60px-Semaphore_Mike.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Semaphore_November.svg/60px-Semaphore_November.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Semaphore_Oscar.svg/60px-Semaphore_Oscar.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Semaphore_Papa.svg/60px-Semaphore_Papa.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Semaphore_Quebec.svg/60px-Semaphore_Quebec.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Semaphore_Romeo.svg/60px-Semaphore_Romeo.svg.png" /></td></tr><tr><td>M</td><td>N</td><td>O</td><td>P</td><td>Q</td><td>R</td></tr><tr><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/9/94/Semaphore_Sierra.svg/60px-Semaphore_Sierra.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Semaphore_Tango.svg/60px-Semaphore_Tango.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Semaphore_Uniform.svg/60px-Semaphore_Uniform.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Semaphore_Victor.svg/60px-Semaphore_Victor.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/8/83/Semaphore_Whiskey.svg/60px-Semaphore_Whiskey.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Semaphore_X-ray.svg/60px-Semaphore_X-ray.svg.png" /></td></tr><tr><td>S</td><td>T</td><td>U</td><td>V</td><td>W</td><td>X</td></tr><tr><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Semaphore_Yankee.svg/60px-Semaphore_Yankee.svg.png" /></td><td><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/2/26/Semaphore_Zulu.svg/60px-Semaphore_Zulu.svg.png" /></td></tr><tr><td>Y</td><td>Z</td></tr></tbody></table></div><br /><br />9:00 => P<br />6:07 => E<br />10:45 => O<br />(the 4th clock)<br />7:45 => H<br />7:52 =>I<br />4:37 => N<br /><br />The word would be PEOPHIN (which is a name of a pet species). Therefore, the 4th letter is P which is the same as the first one. The answer is <span style="font-weight: bold;">9:00</span>.<br /><br /><u>Results</u>: 1885 people guessed the correct answer earning themselves <b>1062 NP</b> each.<br /><br /><span style="font-weight: bold;">References:</span><br />[1] <a href="http://en.wikipedia.org/wiki/Flag_semaphore#Characters">Flag Semaphore Characters</a></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-6008012634942200680?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com22tag:blogger.com,1999:blog-774738449594515927.post-121737070397714012008-09-25T16:15:00.000-07:002008-10-09T21:06:01.486-07:00Date Released: September 25th, 2008.<br />Date Rewarded: October 2nd, 2008.<br /><br />A Chomby was walking down a path one day when Jhudora appeared in front of it. "Solve this puzzle, and you may pass," she said.<br /><br />Suppose a₁ is the first digit (after the decimal point) of Pi, a₂ is the second digit, and so on...<br /><br />What would the following formula equal:<br /><div style="text-align: center;">(a₁ - a₂) * (a₂ - a₃) * (a₃ - a₄) * ... * (a₉₉ - a₁₀₀)<br /></div><br /><b>What is the answer?</b><br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/fur_table_flatfruit.gif" /><br /><u>Flatfruit Table</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution280')"><u>Click to show/hide hints</u></a><br /><div class="commenthidden" id="Solution280"><br />The numerical value of PI truncated to 100 decimal places [1] is:<br /><br />3.1415926535 8979323846 264<span style="font-weight: bold; color: rgb(255, 0, 0);">33</span>83279 502<span style="font-weight: bold; color: rgb(255, 0, 0);">88</span>41971 693<span style="font-weight: bold; color: rgb(255, 0, 0);">99</span>37510 58209749<span style="font-weight: bold; color: rgb(255, 0, 0);">44</span> 5923078164 06286208<span style="font-weight: bold; color: rgb(255, 0, 0);">99</span> 8628034825 342<span style="font-weight: bold; color: rgb(255, 0, 0);">11</span>70679<br /><br />We notice that a₂₄ = a₂₅ = 3. Therefore the formula equal to:<br /><div style="text-align: center;">(a₁ - a₂) * (a₂ - a₃) * ... * (a₂₃ - a₂₄) * 0 * (a₂₅ - a₂₆) * ... * (a₉₉ - a₁₀₀) = 0</div><br />There are several other pairs of consecutive digits that are the same. The answer is <span style="font-weight: bold;">0</span>.<br /><br /><u>Results</u>: 6249 people guessed the correct answer earning themselves <b>321 NP</b> each.<br /><br /><span style="font-weight: bold;">References:</span><br />[1] <a href="http://www.research.att.com/%7Enjas/sequences/A000796">Decimal expansion of PI</a></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-12173707039771401?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com13tag:blogger.com,1999:blog-774738449594515927.post-14829938430009141912008-09-18T19:34:00.000-07:002008-10-11T08:16:58.840-07:00Date Released: September 18th, 2008.<br />Date Rewarded: September 25th, 2008.<br /><p>A Chomby was walking down a path one day when Jhudora appeared in front of it. "Solve this puzzle, and you may pass," she said.</p> <p>Add up all of the previous Lenny Conundrum answers where the answer could be expressed as a number. If the answer was more than one number, pick the lower of the two answers. Take the square root of that sum, round to the nearest integer, and replace the digits as follows:</p> <p>1 : G<br />2 : A if preceded by an odd digit, P if preceded by an even digit<br />3 : H if preceded by an odd digit, R if preceded by an even digit<br />4 : T if preceded by an odd digit, Y if preceded by an even digit<br />5 : O if preceded by an odd digit, E if preceded by an even digit.<br />6 : N<br />7 : D<br />8 : U if preceded by an odd digit, I if preceded by an even digit.<br />9 : S if preceded by an odd digit, W if preceded by an even digit.<br />0 : L if preceded by an odd digit, M if preceded by an even digit.</p> <p>Then, unscramble these letters to find a Neopian word. <b>What is the word?</b> Please only submit a single word, with no other information or punctuation, or your answer may be disqualified.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/fur_rainbow_chair.gif" /><br /><u>Rainbow Arm Chair</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution279')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution279"><br />The biggest number that can contribute to the sum is in Round 111 (294,215,686,440,197,000,000), the second biggest number is in <a href="http://lennyconundrumsolutions.blogspot.com/2008/07/round-269.html">Round 269</a> (52,907,904,000). Other numbers are insignificant to the biggest number. If we take the square root of the biggest number, we get 17,152,716,591. If we take the square root of the sum of the two biggest numbers, we get 17,152,716,592. Therefore, other numbers do not affect the result. It has been verified by adding all numbers in all rounds.<br /><br />Using 17,152,716,592 to decode, we get GDGOADGNESA. It is not supposed to be what TNT intended. It should be GDG<span style="font-weight: bold; color: rgb(255, 0, 0);">A</span>ADG<span style="font-weight: bold; color: rgb(255, 0, 0);">M</span>ESA or GDG<span style="font-weight: bold; color: rgb(255, 0, 0);">M</span>ADG<span style="font-weight: bold; color: rgb(255, 0, 0);">A</span>ESA. With either one of them, the answer is <span style="font-weight: bold;">gadgadsgame</span>. Here is what TNT said:<br /><blockquote>Actually, there was an error in the puzzle that we did not notice until after the Lenny Conundrum went live, so we accepted many different answers that had "Gadgads" in it.</blockquote><u>Results</u>: 1325 people guessed the correct answer earning themselves <b>1510 NP</b> each.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-1482993843000914191?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com36tag:blogger.com,1999:blog-774738449594515927.post-73693398636784225822008-09-11T15:04:00.000-07:002008-10-10T08:29:46.858-07:00Date Released: September 11th, 2008.<br />Date Rewarded: September 18th, 2008.<br /><p><b>What percentage of users answering this question will get it correct?</b></p> <p>Please round to the nearest whole number. Please do not include any characters in your answer other than numbers. This includes spaces, punctuation, or percentage signs. If there is no correct answer, we'll pick whatever answer comes closest to being correct. And yes, we're intentionally asking this question again.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/fur_funky_sofa.gif" /><br /><u>Funky Blue and Orange Sofa</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution278')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution278"><br />Another guessing game. Last week answer is 3 so a lot of people went with 3. Here is the solution from TNT<br /><p>19,427 users entered this week's Lenny Conundrum. Here were the top twelve answers, with the rounded percentage of users answering each one:<br /></p><ol><li>"3" (2517 guesses, 13.0% of total entries)</li><li>"5" (1498 guesses, 7.7% of total entries)</li><li>"4" (1429 guesses, 7.4% of total entries)</li><li>"100" (1258 guesses, 6.5% of total entries)</li><li>"2" (1244 guesses, 6.4% of total entries)</li><li>"1" (924 guesses, 4.8% of total entries)</li><li>"6" (505 guesses, 2.6% of total entries)</li><li>"7" (444 guesses, 2.3% of total entries)</li><li>"50" (431 guesses, 2.2% of total entries)</li><li>"0" (418 guesses, 2.2% of total entries</li><li>"10" (402 guesses, 2.1% of total entries</li><li>"8" (226 guesses, 1.2% of total entries</li></ol><br />All other guesses came in at under 2%, and since 0, 1, and 2 are already accounted for in the top ten, it's just a matter of which one comes closest. From above, you can see that "0" came closest to its corresponding percentage, so 0 was the correct answer.<br /><br /><u>Results</u>: 418 people guessed the correct answer earning themselves <b>4785 NP</b> each. </div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-7369339863678422582?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com8tag:blogger.com,1999:blog-774738449594515927.post-84638692954722638362008-09-04T16:23:00.000-07:002008-10-10T08:21:54.100-07:00Date Released: September 4th, 2008.<br />Date Rewarded: September 11th, 2008.<br /><p><b>What percentage of users answering this question will get it correct?</b></p> <p>Please round to the nearest whole number. Please do not include any characters in your answer other than numbers. This includes spaces, punctuation, or percentage signs. If there is no correct answer, we'll pick whatever answer comes closest to being correct.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/fur_pinklenny_painting.gif" /><br /><u>Pink Lenny Painting</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution277')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution277"><br />It is a guessing game. The following is the solution from TNT.<br /><br />19,948 users entered this week's Lenny Conundrum. Here were the top ten answers, with the rounded percentage of users answering each one:<br /><ol><li>"100" (1370 guesses, 6.9% of total entries)</li><li>"1" (1141 guesses, 5.7% of total entries)</li><li>"3" (821 guesses, 4.1% of total entries)</li><li>"0" (766 guesses, 3.8% of total entries)</li><li>"2" (668 guesses, 3.4% of total entries)</li><li>"50" (654 guesses, 3.3% of total entries)</li><li>"5" (571 guesses, 2.8% of total entries)</li><li>"10" (525 guesses, 2.6% of total entries)</li><li>"4" (460 guesses, 2.3% of total entries)</li><li>"100%" (366 guesses, 1.8% of total entries, but DISQUALIFIED since the question stated to omit percentage signs)</li></ol><br />All other guesses came in at under 2%, and since 0, 1, and 2 are already accounted for in the top ten, it's just a matter of which one comes closest. From above, you can see that "3" came closest to its corresponding percentage, so <span style="font-weight: bold;">3</span> was the correct answer. Wouldn't be interesting to see how people would answer this question already knowing how people answered it before?<br /><br /><u>Results</u>: 821 people guessed the correct answer earning themselves <b>2437 NP</b> each.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-8463869295472263836?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com34tag:blogger.com,1999:blog-774738449594515927.post-79538058747957735482008-08-28T00:32:00.000-07:002008-10-10T08:12:37.521-07:00Date Released: August 28th, 2008.<br />Date Rewarded: September 4th, 2008.<br /><p>The following sentence appears somewhere on the Neopets site. However, only one letter per word is shown here.</p> <div style="text-align: center;"><img src="http://images.neopets.com/games/conundrum/276_oneletter2.gif" /> </div><p><b>What Neopian name can you spell when you unscramble the circled letters?</b> Only submit a single word as your answer; any other information may disqualify your entry.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/ga_kougralily.gif" /><br /><u>Kougra Lily</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution276')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution276"><br />It's funny that the above sentence is from <a href="http://www.neopets.com/games/conundrum.phtml">Lenny Conundrum</a>: "<span style="font-weight: bold; color: rgb(255, 0, 0);">A</span>lso gi<span style="font-weight: bold; color: rgb(255, 0, 0);">v</span>ing ou<span style="font-weight: bold; color: rgb(255, 0, 0);">t</span> the answ<span style="color: rgb(255, 0, 0); font-weight: bold;">e</span>r or o<span style="font-weight: bold; color: rgb(255, 0, 0);">b</span>vious <span style="font-weight: bold; color: rgb(255, 0, 0);">h</span>ints <span style="font-weight: bold; color: rgb(255, 0, 0);">i</span>s a<span style="font-weight: bold; color: rgb(255, 0, 0);">g</span>ainst the <span style="font-weight: bold; color: rgb(255, 0, 0);">r</span>u<span style="font-weight: bold; color: rgb(255, 0, 0);">l</span>es."<br /><br />That leave you with avtebhigrl<span> </span>to unscramble. The answer is <span style="font-weight: bold;">brightvale</span>.<br /><br /><u>Results</u>: 5143 people guessed the correct answer earning themselves <b>389 NP</b> each. </div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-7953805874795773548?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com27tag:blogger.com,1999:blog-774738449594515927.post-70009307943686752152008-08-21T16:18:00.000-07:002008-10-10T07:08:56.671-07:00Date Released: August 21st, 2008.<br />Date Rewarded: August 28th, 2008.<br /><p>You have the following sequence of numbers:<br /><br />24<br />___<br />___<br />9<br />___<br />15<br />19<br /></p> <p>If you multiply the three missing numbers together, what will you get?</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/bam_mat.gif" /><br /><u>Fresh Bamboo Mat</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution275')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution275"><br />Check out the <a href="http://www.neopets.com/calendar.phtml">calendar</a>.<br /><br />* Aug 8th - Blumaroo Day<br />* Aug 11th - Discovery of Brightvale<br />* Aug 18th - Meerca Day!<br />* Aug 20th - Annual Usuki Doll Convention<br />* Aug <span style="font-weight: bold;">24</span>th - Grundo Independence Day<br />* Aug 25th - Mutant Day<br />* Aug 29th - Kyrii Day<br /><br />* Sept <span style="font-weight: bold;">9</span>th - Draik Day<br />* Sept 13th - Techo Day<br />* Sept <span style="font-weight: bold;">15</span>th - The Annual Chocolate Ball<br />* Sept <span style="font-weight: bold;">19</span>th - Poogle Parade (Poogle Day)<br />* Sept 20th - Faerie Festival. Rumour has it that this is when the Faeries are most generous to Neopians.<br />* Sept 23rd - Annual Gormball Championships<br />* Sept 25th - Skeith Day<br /><br />According to the original sequence, the missing numbers are 25, 29 and 13. Therefore, the answer is: 25 * 29 * 13 = <span style="font-weight: bold;">9425</span>.<br /><br /><u>Results</u>: 4405 people guessed the correct answer earning themselves <b>455 NP</b> each. </div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-7000930794368675215?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com5tag:blogger.com,1999:blog-774738449594515927.post-67187914819972631462008-08-14T15:36:00.000-07:002008-10-10T07:04:40.728-07:00Date Released: August 14th, 2008.<br />Date Rewarded: August 21st, 2008.<br /><p>A Chomby was walking down a path one day when Jhudora appeared in front of it. "Solve this puzzle, and you may pass," she said.</p> <p>Suppose you have a bunch of wooden beds, each weighing 200 pounds each, arranged in a pyramid. The base layer is 5 beds by 5 beds, the layer above is 4 beds by 4 beds, and so on until the top layer of one bed. They are arranged in such a way that each bed is resting on four beds below it, one leg on each bed.</p> <p>If the weight on each bed is always equally distributed to all four legs, and each bed leg can only support 200 pounds, how many pounds can you place on top of the topmost bed? Please round to the nearest pound, and plese submit only a single number as your answer.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/brown_bed.gif" /><br /><u>Wooden Bed</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution274')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution274"><br />If the weight on each bed is always equally distributed to all four legs, and each bed leg can only support 200 pounds => Each bed can support maximum 200 x 4 = 800 pounds.<br /><br />Each bed weighs 200 pounds. Let <span style="font-style: italic;">x</span> be the <span>extra</span><span style="font-weight: bold;"> </span>weight you can put on the top of the topmost bed. We will go from top to bottom level.<br /><br /><span style="font-weight: bold;">Top level</span>: total weight = <span style="font-style: italic;">x</span> + 200. Each bed leg can withstands: (<span style="font-style: italic;">x</span> + 200) / 4.<br /><br /><span style="font-weight: bold;">2nd top level</span>: see the below figure for visual help, the four red dots are the four legs of the top level bed. The total weight of each bed (including itself) = (<span style="font-style: italic;">x</span> + 200) / 4 + 200 = (<span style="font-style: italic;">x</span> + 1000) /4. Each bed leg withstands: (<span style="font-style: italic;">x</span> + 1000) / 16.<br /><br /><img style="margin: 0px auto 10px; display: block; text-align: center;" src="http://2.bp.blogspot.com/_I-kT7eLPpXY/SKx-oNRLGoI/AAAAAAAAAHM/LnGK7h-1GQA/s400/round_274_1.png" alt="" id="BLOGGER_PHOTO_ID_5236699695946603138" border="0" /><br /><span style="font-weight: bold;">3rd level</span>: see the below figure for visual help, the red dots are the 2nd top level beds' legs.<br /><br />* middle bed: the bed withstands 4 legs of the above 4 beds (one of each). Therefore, the total weight should be: (<span style="font-style: italic;">x</span> + 1000) / 16 * 4 + 200 = (<span style="font-style: italic;">x</span> + 1800) / 4. Each bed leg withstands: (<span style="font-style: italic;">x</span> + 1800) / 16.<br /><br />* side beds: each bed withstands 2 legs of the above 2 beds (one of each). Therefore, the total weight should be: (<span style="font-style: italic;">x</span> + 1000) / 16 * 2 + 200 = (<span style="font-style: italic;">x</span> + 2600) / 8. Each bed leg withstands: (<span style="font-style: italic;">x</span> + 2600) / 32.<br /><br />* corner beds: each bed withstands 1 leg of the above 1 bed. Therefore, the total weight should be: (<span style="font-style: italic;">x</span> + 1000) / 16 + 200 = (<span style="font-style: italic;">x</span> + 4200) / 16. Each bed leg withstands: (<span style="font-style: italic;">x</span> + 4200) / 64.<br /><br /><img style="margin: 0px auto 10px; display: block; text-align: center;" src="http://3.bp.blogspot.com/_I-kT7eLPpXY/SKyAQy_FNnI/AAAAAAAAAHU/SyMqivu1KXI/s400/round_274_2.png" alt="" id="BLOGGER_PHOTO_ID_5236701492777662066" border="0" /><br /><span style="font-weight: bold;">4th level</span>: see the below figure for visual help, the red dots are the 3rd level middle bed's legs, the yellow dots are the 3rd level side beds' legs and the blue red dots are the 3rd level corner beds' legs.<br /><br />Since we only concern about the bed that withstand the most weights, we can ignore the side and corner beds and only consider the 4 middle beds which contributes most weights into the middle bed on the bottom level (see the bottom level figure). Each of the 4 middle beds withstand 1 leg from a 3rd level corner bed, 2 legs from 3rd level side beds, 1 leg from the 3rd level middle bed. Therefore, the total weight of each 4th level middle bed should be: (<span style="font-style: italic;">x</span> + 1800) / 16 + (<span style="font-style: italic;">x</span> + 2600) / 32 * 2 + (<span style="font-style: italic;">x</span> + 4200) / 64 + 200 = (9<span style="font-style: italic;">x</span> + 34600) / 64. Each bed leg withstands: (9<span style="font-style: italic;">x</span> + 34600) / 256.<br /><br /><img style="margin: 0px auto 10px; display: block; text-align: center;" src="http://4.bp.blogspot.com/_I-kT7eLPpXY/SKyBTjm_t8I/AAAAAAAAAHc/Wmm_lL19NrY/s400/round_274_3.png" alt="" id="BLOGGER_PHOTO_ID_5236702639701342146" border="0" /><br /><span style="font-weight: bold;">Bottom level</span>: see the below figure for visual help, the red dots are the 4th level middle beds' legs, the yellow dots are the 4th level side beds' legs and the blue red dots are the 4th level corner beds' legs.<br /><br />Similar to the 4th level, we only concern with the bed that has the most weight on. That bed is the middle bed. Therefore, the weight of on that bed is: (9<span style="font-style: italic;">x</span> + 34600) / 256 * 4 + 200 = (9<span style="font-style: italic;">x</span> + 47400) / 64. Each bed leg withstands: (9<span style="font-style: italic;">x</span> + 47400) / 256.<br /><br /><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://1.bp.blogspot.com/_I-kT7eLPpXY/SKyDtms8CcI/AAAAAAAAAHs/emPQRxGEBHQ/s400/round_274_4.png" alt="" id="BLOGGER_PHOTO_ID_5236705286231427522" border="0" /><br />We know that each beg leg can only withstand maximum 200 pounds. From all the levels, the bed that has most weights on is the middle bed of the bottom level. Therefore:<br /><div style="text-align: center;">(9<span style="font-style: italic;">x</span> + 47400) / 256 <= 200 <=> <span style="font-style: italic;">x </span><= 3800/9 = 422.22<br /></div><br />Therefore, the answer is <span style="font-weight: bold;">422</span>.<br /><br /><u>Results</u>: 1432 people guessed the correct answer earning themselves <b>1397 NP</b> each. </div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-6718791481997263146?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com22tag:blogger.com,1999:blog-774738449594515927.post-17894267850634094922008-08-07T20:00:00.000-07:002008-10-10T07:32:26.863-07:00Date Released: August 7th, 2008.<br />Date Rewarded: August 14th, 2008.<br /><p>The following sentence appears somewhere on the Neopets site. However, only the vowels are shown here.</p> <div style="text-align: center;"><img src="http://images.neopets.com/games/conundrum/273_vowelsonly.gif" /> </div><p><b>What Neopian name can you spell when you unscramble the circled letters?</b> Only submit a single word as your answer; any other information may disqualify your entry.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/dubloon4.gif" /><br /><u>Ten Dubloon Coin</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution273')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution273"><br />If you check on <a href="http://www.neopets.com/objects.phtml">Neopia Central</a>, you see this "You <span style="font-weight: bold; color: rgb(255, 0, 0);">c</span>an buy foo<span style="font-weight: bold; color: rgb(255, 0, 0);">d</span> or toys for your Neopet, co<span style="font-weight: bold; color: rgb(255, 0, 0);">l</span>lect r<span style="font-weight: bold; color: rgb(255, 0, 0);">a</span>re items, magic<span style="font-weight: bold; color: rgb(255, 0, 0);">a</span>l potions, collecta<span style="font-weight: bold; color: rgb(255, 0, 0);">b</span>le ca<span style="font-weight: bold; color: rgb(255, 0, 0);">r</span>d<span style="font-weight: bold; color: rgb(255, 0, 0);">s</span>, and ev<span style="font-weight: bold; color: rgb(255, 0, 0);">e</span>n buy clothes!"<br /><br />That leave you with <span>cdlaabrse </span>to unscramble. Since the prize is a Dubloon Coin, the Neopian character should be a pirate. It is <span style="font-weight: bold;">Scarblade</span>.<br /><br /><u>Results</u>: 8507 people guessed the correct answer earning themselves <b>236 NP</b> each.<br /></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-1789426785063409492?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com19tag:blogger.com,1999:blog-774738449594515927.post-77083899040379938802008-07-24T17:34:00.000-07:002008-08-20T08:58:32.460-07:00Date Released: July 24th, 2008.<br />Date Rewarded: July 31st, 2008.<br /><p>A Chomby was walking down a path one day when Jhudora appeared in front of it. "Solve this puzzle, and you may pass," she said.</p> <p>Suppose you have four numbered tiles, one with a 3 on it, one with a 4, one with a 5, and one with a 6.</p> <div style="text-align: center;"><img src="http://images.neopets.com/games/conundrum/272_3456.gif" /> </div><p><b>What is the largest four-digit number that can be formed by these tiles that is not evenly divisible by 9?</b> Only submit a four-digit number as your answer; any other information may disqualify your entry.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/boo_faerie_cloudnine.gif" /><br /><u>Faerie Tales: Cloud Nine</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution272')"><u>Click to show/solution</u></a><br /><div class="commenthidden" id="Solution272"><br />A number is divisible by 9 when the sum of its digits is divisible by 9 [1]. If we sum the four given digits: 3 + 4 + 5 + 6 = 18 (which is divisible by 9), there can't be a number of those 4 digits that isn't divisible by 9.<br /><br />However, if you rotate the #6 tile, you get #9. Now, the sum of the digits is 3 + 4 + 5 + 9 = 21 (which is not divisible by 9). Any 4 digit number that formed by the above digits will not be divisible by 9. Therefore, the answer is the largest number formed by those 4 digits (3, 4, 5, 9). It is <span style="font-weight: bold;">9543</span>.<br /><br /><u>Results</u>: some (5503-5517) people guessed the correct answer earning themselves <span style="font-weight: bold;">363</span><b> NP</b> each.<br /><br /><span style="font-weight: bold;">References:</span><br />[1] <a href="http://en.wikipedia.org/wiki/Divisibility_rule#1_through_20">Divisibility rule</a><br /></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-7708389904037993880?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com28tag:blogger.com,1999:blog-774738449594515927.post-63124282704559640742008-07-17T16:30:00.000-07:002008-10-09T07:26:38.598-07:00Date Released: July 17th, 2008.<br />Date Rewarded: July 24th, 2008.<br /><br />Assume the world of Neopia is a spherical planet with a diameter of 1600 km with a uniform density of 5200 kilograms per cubic metre. If the moon of Kreludor is in a geostationary orbit around Neopia, and assuming a Neopian sidereal day is exactly 24 hours, how far is that geostationary orbit above the surface of Neopia?<br /><br />Please submit your answer in kilometres, and round to the nearest kilometre. Submit only a number; any additional information may disqualify your entry.<br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/toy_kreldef_plushie.gif" /><br /><u>Kreludan Defender Plushie</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution271')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution271"><br />This puzzle is about Geostationary orbit. You can find a full explanation about this topic in [1]. The main equation we need to focus on is:<br /><div style="text-align: center;"><span style="font-style: italic;">r</span>³ = <span style="font-style: italic;">G*M</span> / <span style="font-style: italic;">ω</span>²</div><br />where <span style="font-style: italic;">r</span> is the distance between the Neopia's center of mass to the Kreludor moon's geostationary orbit, <span style="font-style: italic;">G</span> = <span style="white-space: nowrap;">6.674 28 * 10^-11 m³/(kg*s²) </span>is the gravitational constant, <span style="font-style: italic;">M</span> is the mass of the Neopia and <span style="font-style: italic;">ω</span> is the angular speed of the moon.<br /><br />The mass of the Neopia planet can be calculated by the following equation:<br /><div style="text-align: center;"><span style="font-style: italic;">M</span> = <span style="font-style: italic;">ρ</span> * <span style="font-style: italic;">V</span> = <span style="font-style: italic;">ρ</span> * 4/3 * pi * <span style="font-style: italic;">R</span>³</div><br />where <span style="font-style: italic;">ρ</span> = 5200 kg/m³is the density of Neopia, <span style="font-style: italic;">V</span> is the volume of the planet, <span style="font-style: italic;"><span style="font-style: italic;"></span>R</span> = <span style="font-style: italic;">d</span>/2 = 800 km = 800,000 m is the radius of the planet.<br /><br />The angular speed of the Kredulor moon can be calculated by the following equation:<br /><div style="text-align: center;"><span style="font-style: italic;">ω</span> = (2 * pi) / 1 sidereal day = (2 * pi) / (24 * 60 * 60) = pi/43200 rad/s<br /></div><br />Therefore, we have:<br /><div style="text-align: center;"><span style="font-style: italic;">r</span>³ = <span style="font-style: italic;">G </span>* <span style="font-style: italic;">ρ</span> * 4/3 * pi * <span style="font-style: italic;">R</span>³ / (pi/43200)² = (86400)² * G * <span style="font-style: italic;">ρ </span> * <span style="font-style: italic;">R</span>³ / (3*pi)<br /><br /></div>Replace numbers into the above equation, then take cubic root, we can get <span style="font-style: italic;">r</span> = 5201692.7355. The answer is the distance from the Neopia planet surface to the orbit. Therefore, it should be:<br /><div style="text-align: center;">distance = (<span style="font-style: italic;">r</span> - <span style="font-style: italic;">R</span>)/1000 = 4401.69<br /></div><br />We use 1000 factor in the above equation because we want to get in kilometers. Round the distance and we get <span style="font-weight: bold;">4402</span> as the answer.<br /><br /><u>Results</u>: 526 people guessed the correct answer earning themselves <b>3803 NP</b> each.<br /><br /><span style="font-weight: bold;">References:</span><br />[1] <a href="http://en.wikipedia.org/wiki/Geostationary_orbit#Derivation_of_geostationary_altitude">Geostationary orbit</a></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-6312428270455964074?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com25tag:blogger.com,1999:blog-774738449594515927.post-82692775450523145022008-07-10T17:54:00.000-07:002008-10-09T21:15:37.531-07:00<p>Date Released: July 10th, 2008.<br />Date Rewarded: July 17th, 2008.</p><p>The Monoceraptor was walking down a path one day when a Babaa appeared in front of it at exactly 8:06 AM. </p><p>The next day, the Monoceraptor was walking down the same path, and the Babaa appeared in front of it at 6:03 PM.</p> <p>The next day, the same thing happened at 11:05 AM.</p> <p>The next three days were at 3:09 PM, 5:05 AM, and 4:01 AM.</p> <p><b>What time did the Babaa appear in front of the Monoceraptor on the seventh day?</b> Submit your answer in the exact same time format as above. For example, if it occured at 9:15 in the evening, you would submit <b>9:15 PM</b>. Do not include any extra information other than your answer.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/nfu_neovia_clock.gif" /><br /><u>Grandfather Clock</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution270')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution270"><br />This is a sequence puzzle. The sequence is: 8:06 AM, 6:03 PM, 11:05 AM, 3:09 PM, 5:05 AM, 4:01 AM.<br /><br />If we write twenty four hours in words and arrange in alphabetical order, it should be: eight (<span style="font-style: italic;">8 AM</span>), eighteen (<span style="font-style: italic;">6 PM</span>), eleven (<span style="font-style: italic;">11 AM</span>), fifteen (<span style="font-style: italic;">3 PM</span>), five (<span style="font-style: italic;">5 AM</span>), four (<span style="font-style: italic;">4 AM</span>), fourteen, nine, nineteen, one, seven, seventeen, six, sixteen, ten, thirteen, three, twelve, twenty one, twenty three, twenty two, two, zero. Therefore, the next hour should be fourteen or 2 PM.<br /><br />For the minutes, notice the PI number: 3.14159265358979323846... The 8th digit is <span style="font-style: italic;">6</span>, the 18th digit is <span style="font-style: italic;">3</span>, the 11th digit is <span style="font-style: italic;">5</span>, the 15th digit is <span style="font-style: italic;">9</span>, the 5th digit is <span style="font-style: italic;">5</span> and the 4th digit is <span style="font-style: italic;">1</span>. Therefore, the next minute should be corresponding to the 14th digit which is 7.<br /><br />The answer is <span style="font-weight: bold;">2:07 PM</span>.<br /><br /><u>Results</u>: 50 people guessed the correct answer earning themselves <b>40,000 NP</b> each.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-8269277545052314502?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com30tag:blogger.com,1999:blog-774738449594515927.post-34876702046110670852008-07-03T22:23:00.000-07:002008-10-09T21:15:14.263-07:00Date Released: July 3rd, 2008.<br />Date Rewarded: July 10th, 2008.<br /><p>The Monoceraptor was walking down a path one day when a babaa appeared in front of it. "Solve this puzzle, and you may pass," it said.</p> <p>Another ancient tomb in the Lost Desert has the following grid engraved on the tomb door:<br /></p><div style="text-align: center;"><img src="http://images.neopets.com/games/conundrum/269_yetanothergrid.gif" /> </div><p></p><p>You must fill in each empty square with a digits from 1-9 such that the vertical sums of the digits match the number above the column, and the horizontal sums match the numbers to the left of the row. No digit will be used more than once in a set. Once you figure out the digits, multiply all of the digits in the circled squares to get your answer.</p> <p><b>What number will you get when you multiply the circled digits?</b> Please submit only a single number as your answer; do not submit ANY information other than the answer. Otherwise, your submission may be disqualified.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/fur_babaa_lamp.gif" /><br /><u>Babaa Lamp</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution269')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution269"><br />This conundrum is actually a Kakuro game [1]. There is a flaw though. If you look at the upper left part with the red number 17. In second row, you have the sum is 21 with 6 blocks. The only choice for the numbers should be 1, 2, 3, 4, 5 and 6. In the fifth column, you have the sum is 17 with 2 blocks. The only choice for the numbers should be 8 and 9. There is no intersection between the above two sets of numbers. Therefore, either number 17 or number 21 should be corrected. People said that TNT intended to make the mistake to prevent people input numbers into a solver.<br /><br />If we correct the red number 17 by number 4, then we can solve the grid as following:<br /><br /><img style="margin: 0px auto 10px; display: block; text-align: center;" src="http://bp3.blogger.com/_I-kT7eLPpXY/SGz1qGcFf4I/AAAAAAAAAG0/UtyHl48FKgM/s400/round_269_1.png" alt="" id="BLOGGER_PHOTO_ID_5218816171847286658" border="0" /><br />There are two choices for the numbers that marked with '<span style="font-style: italic; font-weight: bold;">X</span>'<br /><br /><img style="margin: 0px auto 10px; display: block; text-align: center;" src="http://bp0.blogger.com/_I-kT7eLPpXY/SGz25Gee4LI/AAAAAAAAAHE/5gMn4reNK8A/s400/round_269_2.png" alt="" id="BLOGGER_PHOTO_ID_5218817529067004082" border="0" /><br />If you multiply the numbers in orange color blocks:<br /><div style="text-align: center;">answer = 1 * 2² * 3⁵ * 4² * 5³ * 6 * 7 * 8 * 9² = <span style="font-weight: bold;">52907904000</span><br /></div><br /><u>Results</u>: 1536 people guessed the correct answer earning themselves <b>1303</b><b> NP</b> each.<br /><br /><span style="font-weight: bold;">References:</span><br />[1] <a href="http://en.wikipedia.org/wiki/Kakuro">Kakuro</a></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-3487670204611067085?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com29tag:blogger.com,1999:blog-774738449594515927.post-52105721481176467322008-06-26T16:01:00.000-07:002008-08-20T10:08:32.667-07:00Date Released: June 26th, 2008.<br />Date Rewarded: July 2nd, 2008.<br /><p>A Grarrl was walking down a path one day when Illusen appeared in front of it. "Solve this puzzle, and you may pass," she said.</p> <p>Another ancient tomb in the Lost Desert has the following grid of letters engraved on the tomb door:<br /></p><div style="text-align: center;"><img src="http://images.neopets.com/games/conundrum/268_anothergridd.gif" /> </div><p></p><p>If the correct letters are engraved on the tomb door, it will open. However, the last column of letters is missing.</p> <p><b>If you figure out what the missing letters are and read down the last column of letters, what will it spell?</b> For example, if the last column's letters were A, B, C, D, E, and F, you would submit "ABCDEF". Please submit your answer with NO SPACES; do not submit ANY information other than the answer. Otherwise, your submission may be disqualified.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/boo_spelling.gif" /><br /><u>Basic Spelling Songs</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution268')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution268"><br />If you convert the letters into numbers using the following scheme, you will get a grid of numbers.<br /><div style="text-align: center;">A = 1, B = 2, C = 3, ... X = 24, Y = 25, Z = 26</div><br />The grid of numbers is:<br /><br /><div style="text-align: center;"><table align="center" border="1"><tbody align="right"><tr><td width="25">3</td><td width="25">11</td><td width="25">19</td><td width="25">1</td><td width="25">9</td><td width="25"><span style="font-weight: bold; color: rgb(255, 0, 0);">17</span></td></tr><tr><td>3</td><td>13</td><td>23</td><td>7</td><td>17</td><td><span style="color: rgb(255, 0, 0); font-weight: bold;">1</span></td></tr><tr><td>11</td><td>23</td><td>9</td><td>21</td><td>7</td><td><span style="font-weight: bold; color: rgb(255, 0, 0);">19</span></td></tr><tr><td>9</td><td>23</td><td>11</td><td>25</td><td>13</td><td><span style="color: rgb(255, 0, 0); font-weight: bold;">1</span><br /></td></tr><tr><td>10</td><td>26</td><td>16</td><td>6</td><td>22</td><td><span style="font-weight: bold; color: rgb(255, 0, 0);">12</span></td></tr><tr><td>16</td><td>8</td><td>26</td><td>18</td><td>10</td><td><span style="font-weight: bold; color: rgb(255, 0, 0);">2</span><br /></td></tr></tbody></table></div><br />Notice that in the first row, each number is larger than its previous number by 8, i.e. 11 = 3 + 8, 19 = 11 + 8... Also, if a number is greater than 26, it can be converted into a modulo [1] of 26 (or subtracted by 26). In this case 19 + 8 = 27 and 27 <span style="font-style: italic;">mod </span>26 = 1 (or 27 - 26 = 1). So, you can find the last number by adding 8 into the fifth number in the first row (<span style="font-style: italic;">mod</span> 26 if necessary)<br /><p></p><p>In the second row, similar to the first row, but you need to add 10 (and do 26-modulo operation if necessary). Third row, add 12 (<span style="font-style: italic;">mod </span>26 if necessary). Forth row, add 14 (<span style="font-style: italic;">mod </span>26 if necessary). Fifth row, add 16 (<span style="font-style: italic;">mod</span> 26 if necessary). Last row, add 18 (<span style="font-style: italic;">mod </span>26 if necessary).</p><p>After you get all the numbers in the last column, convert them back into letters using the above mapping technique. The answer is <span style="font-weight: bold;">QASALB</span>.<br /></p><p><u>Results</u>: 5199 people guessed the correct answer earning themselves <b>385</b><b> NP</b> each.</p><p><span style="font-weight: bold;">References:</span><br />[1] <a href="http://en.wikipedia.org/wiki/Modulo_operation">Modulo operation</a></p></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-5210572148117646732?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com24tag:blogger.com,1999:blog-774738449594515927.post-29055496282401597282008-06-19T16:54:00.000-07:002008-10-09T21:14:12.369-07:00Date Released: June 19th, 2008.<br />Date Rewarded: June 26th, 2008.<br /><p>Jhudora was walking down a path one day when a Chomby appeared in front of it. "Solve this puzzle, and you may pass," it said.</p><p>An ancient tomb in the Lost Desert has the following grid of numbers engraved on the tomb door:</p><br /><div style="text-align: center;"><img src="http://images.neopets.com/games/conundrum/267_chombyspuzzle.gif" /> </div><p></p><p>If the correct numbers are engraved on the tomb door, it will open. However, one of these numbers is wrong.</p> <p><b>If you take the wrong number on this grid, and multiply it by the number it should be, what number would you get?</b> For example, if the wrong number was 456 and you knew the correct number was 465, you would multiply the two and submit the answer "212040". Please only submit the answer as a number; do not show your work, or submit ANY information other than the answer. Otherwise, your submission may be disqualified.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/lds_desert_map_scroll.gif" /><br /><u>Lost Desert Map Scroll</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution267')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution267"><br />If you sort the number in the ascending order, you will get:<br /><div style="text-align: center;">6, 15, 35, 77, 143, 221, 323, 437, 667, 897, 1147, 1517, 1763, 2021, 2491, 3127</div><br />We know that the prime number sequence is:<br /><div style="text-align: center;">2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61 ...</div><br />Notice that:<br /><div style="text-align: center;">2 x 3 = 6<br />3 x 5 = 15<br />5 x 7 = 35<br /></div><br />The number in the sequence is the product of two consecutive prime numbers. Therefore, you can continue to test out the sequence until you find the wrong number in the sequence. It is 29 x 31 = 899, not 897. Therefore, the answer should be:<br /><div style="text-align: center;">897 x 899 = <span style="font-weight: bold;">806403</span></div><br /><u>Results</u>: 4024 people guessed the correct answer. (earning themselves <b>498</b><b> NP</b> each)</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-2905549628240159728?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com18tag:blogger.com,1999:blog-774738449594515927.post-46895422489716113912008-06-12T17:35:00.000-07:002008-06-25T16:29:40.656-07:00Date Released: June 12th, 2008.<br />Date Rewarded: June 19th, 2008.<br /><p>A Chomby was walking down a path one day when Jhudora appeared in front of it. "Solve this puzzle, and you may pass," she said.</p> <p>You are presented with the following gibberish:</p> <p><b>WLTT ZXPYGWO WR IRKBPP PK BOX OPHBVUALPN XR OOX YFHOMXPTL BVCRVDH?</b></p> <p>"Here's a tool to help you," Jhudora said as she handed this to you:</p><br /><center><object type="application/x-shockwave-flash" data="http://images.neopets.com/games/conundrum/266_spinner.swf" width="320" height="320"></object></center><br /><p><b>What is the answer to the coded question?</b> Please submit only a single-word answer.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize<br /><br /></span><img src="http://images.neopets.com/items/vday_chocolates.gif" /><br /><u>Heart Shaped Chocolates</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution266')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution266"><br />Assume the first letter ('<span style="font-style: italic;">W</span>') is correct.<br /><br />Here is the step to decode: move the middle ring of the wheel (you can move it in the flash above) so that the next decoding letter match in that ring matches with the previous decoded letter in the outer ring. The red arrow will point to the next decoded letter in the inner ring. The below steps are examples for the decoding process:<br /><br /><u>Second letter:</u><br />Previous decoded letter: '<span style="font-style: italic;">W</span>'<br />Decoding letter: '<span style="font-style: italic;">L</span>'<br />Decoded letter: '<span style="font-style: italic;">H</span>'<br /><img style="margin: 0px auto 10px; display: block; text-align: center;" src="http://bp0.blogger.com/_I-kT7eLPpXY/SFB2nTxNXEI/AAAAAAAAAF8/bfF3vxCYqPE/s400/round_266_1.png" alt="" id="BLOGGER_PHOTO_ID_5210795186561309762" border="0" /><br /><u>Third letter:</u><br />Previous decoded letter: '<span style="font-style: italic;">H</span>'<br />Decoding letter: '<span style="font-style: italic;">T</span>'<br />Decoded letter: '<span style="font-style: italic;">A</span>'<br /><img style="margin: 0px auto 10px; display: block; text-align: center;" src="http://bp0.blogger.com/_I-kT7eLPpXY/SFB4K1DXZ7I/AAAAAAAAAGE/BG_OXmBH0zI/s400/round_266_2.png" alt="" id="BLOGGER_PHOTO_ID_5210796896302884786" border="0" /><br /><u>Fourth letter:</u><br />Previous decoded letter: '<span style="font-style: italic;">A</span>'<br />Decoding letter: '<span style="font-style: italic;">T</span>'<br />Decoded letter: '<span style="font-style: italic;">T</span>'<br /><img style="margin: 0px auto 10px; display: block; text-align: center;" src="http://bp1.blogger.com/_I-kT7eLPpXY/SFB7K12spKI/AAAAAAAAAGU/OEucLQakoes/s400/round_266_3.png" alt="" id="BLOGGER_PHOTO_ID_5210800195053069474" border="0" /><br />Therefore, the first word is '<span style="font-style: italic;">WHAT</span>'. If you do the rest of the sequence of letters, the question is '<span style="font-style: italic;">WHAT SPECIES OF NEOPET IS THE SHOPKEEPER OF THE CHOCOLATE FACTORY</span>?'. The answer is <span style="font-weight: bold;">Kiko</span>.<br /><br /><u>Results</u>: 3769 people guessed the correct answer earning themselves <b>531</b><b> NP</b> each.<br /></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-4689542248971611391?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com32tag:blogger.com,1999:blog-774738449594515927.post-58577589479585792572008-06-05T18:58:00.000-07:002008-06-12T09:22:24.286-07:00<p>Date Released: June 5th, 2008.<br />Date Rewarded: June 12th, 2008.<br /></p><p>A Chomby was walking down a path one day when Jhudora appeared in front of it. "Solve this puzzle, and you may pass," she said.</p><br /><div style="text-align: center;"><img src="http://images.neopets.com/games/clicktoplay/ctp_999.gif" /> </div><p>Suppose you're playing Destruct-O-Match III, and, on level one of Classic mode, you find that every block is the same colour! </p><p><b>How many points will you get for completing level one, assuming no powerups?</b> Please submit only a number as your answer, with no extra information, or your answer may be disqualified.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize<br /><br /></span><img src="http://images.neopets.com/items/sta_destructo.gif" /><br /><u>Destruct-O-Match Stamp</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution265')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution265"><br />In Classic mode and level 1, if you destroy more than 15 blocks at a time (without a powerup), the number of points you get is twice of the number of destroyed blocks. If you clear all the blocks, you also get 100 bonus points. The whole wall is a rectangle of 14 block wide and 12 block high. The number of points you will get is<br /><div style="text-align: center;">points = 14 * 12 * 2 + 100 = <span style="font-weight: bold;">436</span></div><br /><u>Results</u>: 4151 people guessed the correct answer earning themselves <b>482</b><b> NP</b> each.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-5857758947958579257?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com10tag:blogger.com,1999:blog-774738449594515927.post-12355254876407150052008-05-29T18:27:00.000-07:002008-10-09T21:10:34.530-07:00Date Released: May 29th, 2008.<br />Date Rewarded: June 5th, 2008.<br /><br />A Chomby was walking down a path one day when Jhudora appeared in front of it. "Solve this puzzle, and you may pass," she said. <p>What is the missing word in this sequence?<br />allowed<br />here<br />entry<br />________<br />you<br />here<br />you </p><p>Please enter only a single word, with no other information. Otherwise, your entry will be disqualified.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize<br /><br /></span><img src="http://images.neopets.com/items/boo_skeith_secrets.gif" /><br /><u>Top Secret Skeith Stuff</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution264')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution264"><br />Check out the <a href="http://www.neopets.com/neoboards/index.phtml">Neoboards</a> and the description of each board:<br /><br />Avatars/Neosignatures: ... Item pools are a scam and are not <span style="font-weight: bold; color: rgb(255, 0, 0);">allowed</span>!<br />Battledome: ... Anything and everything Battledome is in <span style="font-weight: bold; color: rgb(255, 0, 0);">here</span>.<br />Beauty Contest: ... regarding YOUR OWN Beauty Contest <span style="font-weight: bold; color: rgb(255, 0, 0);">entry</span>!)<br />Customisation: ... that would be <span style="font-weight: bold;">embarassing</span>.<br />Evil Things and Monster Sightings: ... This board is for<span style="font-weight: bold;"> <span style="color: rgb(255, 0, 0);">you</span></span>.<br />Fan Clubs: ... Discuss it <span style="font-weight: bold; color: rgb(255, 0, 0);">here</span>!<br />Games: ... Yup, the Games board is for <span style="font-weight: bold; color: rgb(255, 0, 0);">you</span>.<br /><br />Each word in the sequence is the last word of each board's description. Therefore, answer should be <span style="font-weight: bold;">embarassing</span>. Note that the answer is a common misspelling word.<br /><br /><u>Results</u>: 3983 people guessed the correct answer earning themselves <b>503</b><b> NP</b> each.<br /></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-1235525487640715005?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com15tag:blogger.com,1999:blog-774738449594515927.post-41800427732241236242008-05-22T15:11:00.000-07:002008-10-09T21:11:40.034-07:00Date Released: May 22nd, 2008.<br />Date Rewarded: May 29th, 2008.<br /><p>A Chomby was walking down a path one day when Jhudora appeared in front of it. "Solve this puzzle, and you may pass," she said.</p> <p>What is the next number in this sequence?<br />1<br />721<br />727<br />5767<br />5791<br />5792<br />___ </p><p>Please enter only a single number, with no other information. Otherwise, your entry will be disqualified.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize<br /><br /></span><img src="http://images.neopets.com/items/hotdog_2.gif" /><br /><u>Megachilli Hot Dog</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution263')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution263"><br />First, you subtract the number to the previous number (assume that the number before the first one is 0). The sequence becomes:<br /><div style="text-align: center;">1 721 727 5767 5791 5792 -> 1 720 6 5040 24 1.<br /></div><br />We realize that 1 = 0! = 1!, 6 = 3!, 24 = 4!, 720 = 6!, 5040 = 7!, where ! is factorial [1].<br /><br />Therefore, the original sequence can be decomposed at:<br />1 = 1! or (0!)<br />721 = 1! + 6!<br />727 = 1! + 6! + 3!<br />5767 = 1! + 6! + 3! + 7!<br />5791 = 1! + 6! + 3! + 7! + 4!<br />5792 = 1! + 6! + 3! + 7! + 4! + 1!<br />next number = 1! + 6! + 3! + 7! + 4! + 1! + <span style="font-style: italic;">n</span>!<br /><br />So, the sequence becomes:<br /><div style="text-align: center;">1! (or 0!) 6! 3! 7! 4! 1! (or 0!) <span style="font-style: italic;">n</span>!</div><br />Temporarily ignore the factorial sign and 'or 0!' part, we can rewrite the sequence as:<br /><div style="text-align: center;">1 6 3 7 4 1 <span style="font-style: italic;">n</span></div><br />The sequence is the number of letters in each word of the first sentence of the puzzle.<br /><div style="text-align: center;">"A Chomby was walking down a path one day..."<br /></div><br />Therefore, <span style="font-style: italic;">n</span> is 4. The next number should be: 1! + 6! + 3! + 7! + 4! + 1! + 4! = <span style="font-weight: bold;">5816</span>.<br /><br /><u>Results</u>: 1167 people guessed the correct answer earning themselves <b>1714</b><b> NP</b> each.<br /><br /><span style="font-weight: bold;">References:</span><br />[1] <a href="http://en.wikipedia.org/wiki/Factorial">Factorial</a><br /></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-4180042773224123624?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com21tag:blogger.com,1999:blog-774738449594515927.post-37129941400085198262008-05-15T15:25:00.000-07:002008-10-09T07:25:34.281-07:00Date Released: May 15th, 2008.<br />Date Rewarded: May 22nd, 2008.<br /><p>A Chomby was walking down a path one day when Jhudora appeared in front of it. "Solve this puzzle, and you may pass," she said.</p> <p>How many people did not properly follow the instructions on last week's Lenny Conundrum, and submitted more than a single word when the Conundrum specifically required a one-word answer?</p> <p>Please round to the nearest 50, and please submit only a number, otherwise you will be disqualified like all those people from last week.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize<br /><br /></span><img src="http://images.neopets.com/items/boo_sloth_rules.gif" /><br /><u>Rules to Rule By</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution262')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution262">It's just a guessing game basically. You can guess number in 50 increment: 0, 50, 100, 150, 200, 250... The answer is <span style="font-weight: bold;">750</span>.<br /><br /><u>Results</u>: 180 people guessed the correct answer earning themselves <b>11112</b><b> NP</b> each.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-3712994140008519826?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com17tag:blogger.com,1999:blog-774738449594515927.post-43680825726344668392008-05-08T16:56:00.000-07:002008-10-09T21:12:06.450-07:00Date Released: May 8th, 2008.<br />Date Rewarded: May 15th, 2008.<br /><br /><p style="text-align: center;"><img src="http://images.neopets.com/items/food_veg_radish.gif" /> <img src="http://images.neopets.com/items/foo_porridge.gif" /></p><br />What's the next word in this sequence?<br /><br />Cream<br />Radish<br />And<br />______ <p>Submit only a one-word answer.</p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize<br /><br /></span><img src="http://images.neopets.com/items/healthy_radish_3.gif" /><br /><u>Radish Meringue</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution261')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution261"><br />Check out<br /><a href="http://www.neopets.com/water/restaurant.phtml?type=waitress"><img src="http://images.neopets.com/water/kelplogo.gif" alt="Kelp" border="0" /></a><br /><br />The 1^st item in <a href="http://www.neopets.com/water/restaurant.phtml?type=1">Appertisers</a>: Maraquan <span style="font-weight: bold; color: rgb(255, 0, 0);">Cream</span> Broth.<br />The 2^nd item in <a href="http://www.neopets.com/water/restaurant.phtml?type=2">Main Courses</a>: Spicy <span style="font-weight: bold; color: rgb(255, 0, 0);">Radish</span> Salad.<br />The 3^rd item in <a href="http://www.neopets.com/water/restaurant.phtml?type=2">Desserts</a>: Peachpa <span style="font-weight: bold; color: rgb(255, 0, 0);">and</span> Stramberry Shell.<br /><br />We observe that the words in the sequence are the second word in the 1^st, 2^nd and 3^rd items on the 1^st, 2^nd and 3^rd menu. Therefore, the next word should be the second word in the 4^th items on the 4^th menu (<a href="http://www.neopets.com/water/restaurant.phtml?type=4">Cocktails</a>): Phear <span style="font-weight: bold;">Juice</span> Tonic.<br /><br /><u>Results</u>: 3477 people guessed the correct answer earning themselves <b>576 NP</b> each.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-4368082572634466839?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com12tag:blogger.com,1999:blog-774738449594515927.post-16408757186605463972008-05-01T17:19:00.000-07:002008-10-09T07:24:50.496-07:00Date Released: May 1st, 2008.<br />Date Rewarded: May 8th, 2008.<br /><br />A Chomby was walking down a path one day when Jhudora appeared in front of it. "Solve this puzzle, and you may pass," she said.<br /><br />Suppose you have a very long steel bar, with a regular pentagonal cross-section where each side of the pentagon is 2 cm in length. This bar will be suspended vertically over a very deep chasm. At the bottom end of the steel bar, there is a spherical steel weight with a diameter of 50 cm. Going up the bar, at every 3 metre increment, there is a spherical steel weight with a diameter of 30cm.<br /><br />If the density of the steel is exactly 7.8 g/cm³, the steel can withstand a tensile stress of 400 MPa, and gravity is 9.81m/s², <b>what is the maximum possible length, in metres, that the bar can extend without breaking?</b> Round <i>down</i> to the nearest metre, submit <i>only a number</i> (with no additional or extraneous information), and disregard any deformation of the bar or any other forces acting on the bar.<br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize<br /><br /></span><img src="http://images.neopets.com/items/foo_negg_armored.gif" /><br /><u>Steel Negg</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution260')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution260"><br />Using the stress equation [1]:<br /><div style="text-align: center;"><span style="font-style: italic;">rho</span> = <span style="font-style: italic;">F</span>/<span style="font-style: italic;">A</span><br /><br /><div style="text-align: left;">where <span style="font-style: italic;">rho</span> = 400 MPa = 400,000,000 kg/m·s² is the tensile stress that steel can withstand, <span style="font-style: italic;">F</span> is the force that the steel has to withstand and <span style="font-style: italic;">A</span> is the crossed area of the steel bar.<br /></div><br /><div style="text-align: left;">The crossed area is a regular pentagon can be calculated by the following equation [2]:<br /></div><div style="text-align: center;"><span style="font-style: italic;">A</span> = 5/4 <span style="font-style: italic;">t</span>² tan(54°) = 0.000688190960236 m²<br /><br /></div></div>where <span style="font-style: italic;">t</span> = 2 cm = 0.02 m is the side of the pentagon.<br /><br />Now, we can calculate the force that the steel bar can withstand:<br /><div style="text-align: center;"><span style="font-style: italic;">F</span> = <span style="font-style: italic;">rho</span> * <span style="font-style: italic;">A</span> = <span style="font-style: italic;">rho</span> * 5/4 <span style="font-style: italic;">t</span>² tan(54°)<br /><br /><div style="text-align: left;">Using Newton's gravity law [3], we have:<br /><div style="text-align: center;"><span style="font-style: italic;">F</span> = <span style="font-style: italic;">m</span> * <span style="font-style: italic;">g</span><br /><br /><div style="text-align: left;">Therefore, the mass that the steel bar can widthstand is:<br /><div style="text-align: center;"><span style="font-style: italic;">m</span> = <span style="font-style: italic;">F</span> /<span style="font-style: italic;">g</span> = <span style="font-style: italic;">rho</span> * 5/4 <span style="font-style: italic;">t</span>² tan(54°) / <span style="font-style: italic;">g</span> = 28060.793485650833 kg<br /></div><br />where <span style="font-style: italic;">g</span> = 9.81 m/s² is the gravitational acceleration.<br /><br />Don't round anything yet. The mass is contributed by 3 components: the big sphere m₁, small spheres m₂, and the steel bar m₃. Since all of them are steel, they have the same density. We have:<br /><div style="text-align: center;"><span style="font-style: italic;">m</span>₁ + int(<span style="font-style: italic;">h</span>/3) *<span style="font-style: italic;"> m</span>₂ + <span style="font-style: italic;">m</span>₃ = <span style="font-style: italic;">m</span><br /><=>[<span style="font-style: italic;">V</span>₁ + int(<span style="font-style: italic;">h</span>/3) * <span style="font-style: italic;">V</span>₂ + <span style="font-style: italic;">A</span> * <span style="font-style: italic;">h</span>] * <span style="font-style: italic;">d</span> = <span style="font-style: italic;">m</span></div><br />where <span style="font-style: italic;">h</span> is the length of the steel bar, int is the floor function (every 3 meter, we have one small sphere), <span style="font-style: italic;">d</span> = 7.8 g/cm³ = 7,800 kg/m³ is the density of steel, <span style="font-style: italic;">V</span>₁, <span style="font-style: italic;">V</span>₂ are the volumes of big and small spheres. The volume of the steel bar is the product of the crossed area with the length of the bar.<br /><br />We can calculate <span style="font-style: italic;">V</span>₁, <span style="font-style: italic;">V</span>₂ by the sphere volume formula [4]:<br /><div style="text-align: center;"><span style="font-style: italic;">V</span>₁ = 4/3 * pi * (<span style="font-style: italic;">r</span>₁)³ = 0.065449846949787 m³<br /><span style="font-style: italic;">V</span>₂ = 4/3 * pi * (<span style="font-style: italic;">r</span>₂)³ = 0.014137166941154 m³</div><br />where the radius <span style="font-style: italic;">r</span>₁ = <span style="font-style: italic;">d</span>₁/2 = 25 cm = 0.25 m, <span style="font-style: italic;">r</span>₂ = <span style="font-style: italic;">d</span>₂/2 = 15 cm = 0.15 m. Don't round both volume either. We already know <span style="font-style: italic;">A</span>, so the equation now should be:<br /><div style="text-align: center;"><span style="font-style: italic;">V</span>₁ + int(<span style="font-style: italic;">h</span>/3) * <span style="font-style: italic;">V</span>₂ + <span style="font-style: italic;">A</span> * <span style="font-style: italic;">h</span> = <span style="font-style: italic;">m</span>/<span style="font-style: italic;">d</span><br /><=>int(<span style="font-style: italic;">h</span>/3) * <span style="font-style: italic;">V</span>₂ + <span style="font-style: italic;">A</span> * <span style="font-style: italic;">h</span> = <span style="font-style: italic;">m</span>/<span style="font-style: italic;">d</span> - <span style="font-style: italic;">V</span>₁</div><br />We know the right hand side of the equation but the left hand side is a little bit tricky. So, we can do a method of trial-and-error to test. Solve <span style="font-style: italic;">h</span> by the following equation:<br /><div style="text-align: center;"><span style="font-style: italic;">h</span>/3 * <span style="font-style: italic;">V</span>₂ + <span style="font-style: italic;">A</span> * <span style="font-style: italic;">h</span> = <span style="font-style: italic;">m</span>/<span style="font-style: italic;">d</span> - <span style="font-style: italic;">V</span>₁<div style="text-align: center;"><=>(<span style="font-style: italic;">V</span>₂/3 + <span style="font-style: italic;">A</span>) * <span style="font-style: italic;">h</span> = <span style="font-style: italic;">m</span>/<span style="font-style: italic;">d</span> - <span style="font-style: italic;">V</span>₁<br /><=><span style="font-style: italic;">h</span> = (<span style="font-style: italic;">m</span>/<span style="font-style: italic;">d</span> - <span style="font-style: italic;">V</span>₁)/(<span style="font-style: italic;">V</span>₂/3 + <span style="font-style: italic;">A</span>) = 654.0200901109209 m<br /><br /><div style="text-align: left;">Now round <span style="font-style: italic;">h</span> down to an integer. We then have <span style="font-style: italic;">h</span> = 654 m. Next, test <span style="font-style: italic;">h</span> into the equation int(<span style="font-style: italic;">h</span>/3)* <span style="font-style: italic;">V</span>₂ + <span style="font-style: italic;">A</span> * <span style="font-style: italic;">h</span> = <span style="font-style: italic;">m</span>/<span style="font-style: italic;">d</span> - <span style="font-style: italic;">V</span>₁. If the left hand side is smaller than the right hand side, the steel bar can withstand the gravitational forces. The largest <span style="font-style: italic;">h</span> that is satisfied that the left hand side is smaller than the right hand side will be the answer.<br /><br />Using <span style="font-style: italic;">h</span> = 654 m, the left hand side: int(<span style="font-style: italic;">h</span>/3)* <span style="font-style: italic;">V</span>₂ + <span style="font-style: italic;">A</span> * <span style="font-style: italic;">h </span>= 3.5320. The right hand side: <span style="font-style: italic;">m</span>/<span style="font-style: italic;">d</span> - <span style="font-style: italic;">V</span>₁ = 3.5321 (good). Now increase <span style="font-style: italic;">h</span> by 1 (<span style="font-style: italic;">h</span> = 655 m) to see if the steel bar can still withstand. The left hand side: int(<span style="font-style: italic;">h</span>/3)* <span style="font-style: italic;">V</span>₂ + <span style="font-style: italic;">A</span> * <span style="font-style: italic;">h </span>= 3.5327. The right hand side: <span style="font-style: italic;">m</span>/<span style="font-style: italic;">d</span> - <span style="font-style: italic;">V</span>₁ = 3.5321. (not good). Therefore, the answer is <span style="font-style: italic;">h</span> = <span style="font-weight: bold;">654</span> m.<br /><br /><u>Results</u>: 986 people guessed the correct answer earning themselves <b>2029 NP</b> each.<br /><br /><span style="font-weight: bold;">References:</span><br />[1] <a href="http://en.wikipedia.org/wiki/Stress_%28physics%29">Stress</a><br />[2] <a href="http://en.wikipedia.org/wiki/Pentagon#Regular_pentagons">Regular pentagon area</a><br />[3] <a href="http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation#Gravitational_field">Newton's gravity law</a><br />[4] <a href="http://en.wikipedia.org/wiki/Sphere#Equations_in_R3">Sphere volume</a></div></div></div></div></div></div></div></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-1640875718660546397?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com31tag:blogger.com,1999:blog-774738449594515927.post-79987404829417045492008-04-24T16:25:00.000-07:002008-06-12T09:10:48.562-07:00Date Released: April 24th, 2008.<br />Date Rewarded: May 1st, 2008.<br /><br />A Chomby was walking down a path one day when Jhudora appeared in front of it. "Unscramble these tiles and solve the puzzle, and you may pass," she said.<br /><br /><div style="text-align: center;"><img src="http://images.neopets.com/games/conundrum/259_scrambledtilesagain.gif" /></div><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize<br /><br /></span><img src="http://images.neopets.com/items/boo_speaktyrannian.gif" /><br /><u>Speak Tyrannian</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution259')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution259"><br /><div style="text-align: center;"><img style="margin: 0px auto 10px; display: block; text-align: center;" src="http://bp0.blogger.com/_I-kT7eLPpXY/SBoooYELAoI/AAAAAAAAAEY/8JvgztYMcC8/s400/round_259.png" alt="" id="BLOGGER_PHOTO_ID_5195509794245116546" border="0" /></div><br />Same as round 257 except this is a trickier one. The question is: How many neopoints does a game of tyranu evavu cost? The answer is <span style="font-weight: bold;">30</span>.<br /><br /><u>Results</u>: 4335 people guessed the correct answer earning themselves <b>462 NP</b> each.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-7998740482941704549?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com9tag:blogger.com,1999:blog-774738449594515927.post-44388696329420941142008-04-17T15:01:00.000-07:002008-10-09T07:24:26.436-07:00Date Released: April 17th, 2008.<br />Date Rewarded: April 24th, 2008.<br /><br />A Chomby was walking down a path one day when Jhudora appeared in front of it. "Answer this question, and you may pass," she said.<br /><br />Suppose you have a perfectly spherical water tank with an inside diameter of 8.6 metres. If the drain at the bottom of the tank can't handle a hydrostatic pressure of more than 50 kilopascals, what is the maximum volume of water, in litres, that can be contained in the tank? Assume that gravitational acceleration is exactly 9.81 m/s². Please round to the nearest 10 litre increment, and please submit only a number for your answer. (For example, if you calculate the answer to be 16277 litres, submit 16280 as your answer)<br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize<br /><br /></span><img src="http://images.neopets.com/items/boo_korbat_underwater.gif" /><br /><u>Underwater Tour</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution258')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution258"><br />First off, we need to find the maximum height of the water tank that the drain can handle using hydrostatic pressure equation [1]:<br /><div style="text-align: center;"><span style="font-style: italic;">P</span> = <span style="font-style: italic;">rho</span> * <span style="font-style: italic;">g</span> * <span style="font-style: italic;">h</span> <=> <span style="font-style: italic;">h</span> = <span style="font-style: italic;">P</span> / (<span style="font-style: italic;">rho</span> * g) = 5.096839959225281 m</div><br />where <span style="font-style: italic;">P</span> = 50k Pa = 50,000 kg/m<span style=";font-family:Arial;font-size:12;" >·</span>s²is the maximum hydrostatic pressure, <span style="font-style: italic;">rho</span> = 1000 kg/m³ is density of water, <span style="font-style: italic;">g</span> = 9.81 m/s² is the gravitational acceleration. Remember that do not round <span style="font-style: italic;">h</span> yet.<br /><br />Then, we can start to calculate the partial volume of the sphere by the following formula (explanation of the formula is at the end of the solution):<br /><div style="text-align: center;"><span style="font-style: italic;">V</span> = 1000 * pi * <span style="font-style: italic;">h</span>² * (<span style="font-style: italic;">r</span> - <span style="font-style: italic;">h</span>/3) = 212276.11<br /><div style="text-align: left;"><br />where <span style="font-style: italic;">r</span> = <span style="font-style: italic;">d</span>/2 = 4.3 m, is the radius of the spherical water tank, <span style="font-style: italic;">h</span> is the above maximum height.<br /><br />We know that: 1 m³ = 1000 dm³ = 1000 liters. We have a 1000 factor in the above formula because the answer should be in liters while we calculated in cubic meters. Now perform rounding as the requirements and we get <span style="font-style: italic;">V</span> = <span style="font-weight: bold;">212,280 </span>liters.<br /><br /><u>Results</u>: 462 people guessed the correct answer earning themselves <b>4330 NP</b> each.<br /><br />If you are interested to see how the partial volume of a sphere is derived, you can continue to read. Otherwise stop here.<br /><br /><img style="margin: 0px auto 10px; display: block; text-align: center;" src="http://bp3.blogger.com/_I-kT7eLPpXY/SAa-Dl_BdcI/AAAAAAAAADo/3_xh5V3nSLw/s400/round_258_1.png" alt="" id="BLOGGER_PHOTO_ID_5190044589536409026" border="0" /><br />We can consider the sphere with center at origin (above picture). We cut the partial sphere into small slices. Each slice is a circle, perpendicular to the vertical direction. Using Pythagorean theorem [2], we can calculate area of each circle at a certain height <span style="font-style: italic;">x</span>:<br /><img style="margin: 0px auto 10px; display: block; text-align: center;" src="http://bp2.blogger.com/_I-kT7eLPpXY/SAaLzV_BdaI/AAAAAAAAADY/SI-NjPbftLw/s400/round_258_2.png" alt="" id="BLOGGER_PHOTO_ID_5189989334782145954" border="0" />Then we do integration on the whole vertical direction to add all area of the slices to get the volume. Since we choose the origin at the center of the sphere, the limit of the integration should be from -<span style="font-style: italic;">r</span> to <span style="font-style: italic;">h</span>-<span style="font-style: italic;">r</span><br /><img style="margin: 0px auto 10px; display: block; text-align: center;" src="http://bp1.blogger.com/_I-kT7eLPpXY/SAaMOF_BdbI/AAAAAAAAADg/x5tDo8NPKkc/s400/round_258_3.png" alt="" id="BLOGGER_PHOTO_ID_5189989794343646642" border="0" /><br /><span style="font-weight: bold;">References:</span><br />[1] <a href="http://en.wikipedia.org/wiki/Pressure#Hydrostatic_pressure_.28head_pressure.29">Hydrostatic pressure</a><br />[2] <a href="http://en.wikipedia.org/wiki/Pythagorean_theorem">Pythagorean theorem</a><br /></div></div></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-4438869632942094114?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com14tag:blogger.com,1999:blog-774738449594515927.post-15227362435079854992008-04-10T17:56:00.000-07:002008-06-12T09:08:45.908-07:00Date Released: April 10th, 2008.<br />Date Rewarded: April 17th, 2008.<br /><br />Figure out how to unscramble these tiles to discover this week's Lenny Conundrum<br /><div style="text-align: center;"><img src="http://images.neopets.com/games/conundrum/257_scrambledtiles.gif" /><br /><span style="font-weight: bold;"><br />Prize</span><br /><br /><img src="http://images.neopets.com/items/food_crepe_zeenana.gif" /><br /><u>Zeenana Crepe</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution257')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution257"><br /><div style="text-align: center;"><img style="margin: 0px auto 10px; display: block; text-align: center;" src="http://bp0.blogger.com/_I-kT7eLPpXY/SAaAX1_BdZI/AAAAAAAAADQ/ALz8XSOs1IM/s400/round_257.png" alt="" id="BLOGGER_PHOTO_ID_5189976767707837842" border="0" /></div>One of they way to solve this problem is to print out the picture, use scissors to cut and try to unscramble the letters. The question is: What neopet species is last in alphabetical order? The answer is <span style="font-weight: bold;">Zafara</span>.<br /><br /><u>Results</u>: 2272 people guessed the correct answer earning themselves <b>881 NP</b> each.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-1522736243507985499?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-33726298242532796532008-04-01T11:51:00.000-07:002009-03-22T17:02:29.472-07:00Every week, The Neopets Team (TNT) releases a new Lenny Conundrum puzzle. We will try to post the hints to solve the current Lenny Conundrum puzzle while we don't want to give out the answer directly. Sometimes, solution is given out by us. Other times, the puzzle is solved by others. In any case, we always put the solution so you have chance to guess the answer. Answer will be posted when the contest is over. So, please don't include a specific number/answer in the comments. We will also try to post all the previous solutions of the Lenny Conundrum puzzles.<br /><br />We hope you enjoy our blog and if you have any feedback to improve our blogs, feel free to drop us a comment. Thanks.<br /><br /><span style="font-weight: bold;">Notice</span>: There was a busy time that we thought we had to shut down this blog. Fortunately, we didn't. This is our plan until further notice.<br /><br /><span style="font-weight: bold;">Every Wednesday</span>: we create an entry for those who are interested in discussion. We may or may not be here to put the solution up. If we are here, we will update the solution.<br /><br /><span style="font-weight: bold;">Every weekend</span>: we will guarantee to put the solutions up by weekends, could be earlier than that. You can check back any time. You can use the following feature or feed feature for easier notice.<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-3372629824253279653?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com20tag:blogger.com,1999:blog-774738449594515927.post-56941660423424128782007-02-01T16:28:00.000-08:002008-10-09T07:21:26.958-07:00Date Released: February 1st, 2007.<br />Date Rewarded: February 8th, 2007.<br /><p><b>How many people answered last week's Lenny Conundrum <i>incorrectly?</i> Please round to the nearest 1000.</b></p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize<br /><br /></span><img src="http://images.neopets.com/items/fur_table_guess.gif" /><br /><u>Guess the Card Game Table</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution201')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution201"><br />This is another guessing game. If you are lucky, you guess it right. The answer is <span style="font-weight: bold;">35000</span>.<br /><br /><u>Results</u>: 95 people guessed the correct answer earning themselves <span style="font-weight: bold;">21053</span><b> NP</b> each.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-5694166042342412878?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-12665395928325687352001-09-12T13:46:00.000-07:002008-10-10T14:10:06.453-07:00Date released: September 12th, 2001.<br />Date rewarded: October 5th, 2001.<br /><br />Pawkeet and Mirgle have had their game of <a href="http://www.neopets.com/games/deckball.phtml"><b>Deckball</b></a> rudely interrupted by a filthy braggart pirate. In an attempt to ruin their fun he steals their deckball, loads it into his cannon and fires it off into the distance. <p> </p><center> <img src="http://images.neopets.com/games/conundrum/24_pirate.gif" border="0" width="150" height="150" /> </center> <p> Assuming that the value of gravity on Neopia is 9.8m/s², and that the initial launch velocity of the ball is 100 meters per second, and also assuming that the ball lands on a rocky outcrop at exactly the same altitude as the cannon... </p><br /><b>How many seconds is the deckball in the air?</b><br />(rounding down to the nearest second)<br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution24')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution24"><br />The information in the problem is not enough to solve. If we want to get the answer that TNT gave, we have to assume the given initial velocity is the part in vertical direction. That means:<br /><div style="text-align: center;"><span style="font-style: italic;">v</span><sub style="font-style: italic;">y</sub> = 100 m/s</div><br />According to the trajectory of a projectile equations [1], the time for the deckball to be in the air is:<br /><div style="text-align: center;"><span style="font-style: italic;">t</span> = 2<span style="font-style: italic;">v</span>sin<span style="font-style: italic;">θ</span> / <span style="font-style: italic;">g</span> = 2<span style="font-style: italic;">v_y</span> / <span style="font-style: italic;">g</span><span> = 20.41 s<br /></span></div><br />where <span style="font-style: italic;">θ</span> is the angle of shooting, and <span style="font-style: italic;">g</span> = 9.8m/s² is the Neopia gravity acceleration. After rounding, the answer is <span style="font-weight: bold;">20 seconds</span>.<br /><br /><span style="font-weight: bold;">References:</span><br />[1] <a href="http://en.wikipedia.org/wiki/Trajectory_of_a_projectile">Trajectory of a projectile</a></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-1266539592832568735?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-55887194315002196482001-08-29T08:00:00.000-07:002008-05-14T21:27:52.934-07:00Date released: August 29th, 2001.<br />Date rewarded: September 12th, 2001.<br /><br />The Fontaine sisters are seamstresses by trade. They have been commissioned to create as many 2 by 3 feet rectangular Jolly Roger flags as they can for the pirates in their village, so Loretta Fontaine has gone out to buy cloth to embroider. <p> Dark cloth costs <b>150</b> Neopoints a foot and comes in a roll five feet wide. It can be bought in any length (even down to the inch). She has a total of <b>1,260</b> Neopoints to spend on the cloth. </p><p> </p><center> <img src="http://images.neopets.com/games/conundrum/23_cloth.gif" border="0" height="150" width="150" /> </center> <b><br />How many WHOLE Jolly Roger flags will they be able to make???</b><br /><div style="text-align: center;"><span style="font-weight: bold;"><br />Prize</span><br />Unknown<br /></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution23')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution23"><br />Number of feet of the Dark cloth that the Fontaine sisters can buy:<br /><div style="text-align: center;">1260 / 150 = 8.4 ft<br /></div><br />The area of the bought cloth:<br /><div style="text-align: center;">8.4 * 5 = 42 ft²<br /></div><br />Number of possible whole flags with that area of the cloth:<br /><div style="text-align: center;">42 / (2 * 3) = 7</div><br />However, if we check the below figure, the is no way to make 7 flags from the cloth (each flag must have 2 ft x 3 ft dimension). The sisters can make maximum 6 flags from the cloth.<br /><br /><img style="margin: 0px auto 10px; display: block; text-align: center;" src="http://bp0.blogger.com/_I-kT7eLPpXY/SCu6Q1ZseiI/AAAAAAAAAFI/bnEbfMnobss/s400/round_23.png" alt="" id="BLOGGER_PHOTO_ID_5200454993104894498" border="0" /><br />Therefore, the Fontaine sisters can make <span style="font-weight: bold;">6</span> whole Jolly Roger flags.<br /></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-5588719431500219648?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-5849754702301415932001-08-17T11:57:00.000-07:002008-10-13T12:07:17.037-07:00From TNT:<br /><blockquote><span style="font-weight: bold;">GREAT NEW FEATURE</span> - We are now counting the number of times you come first in a variety of our games. If you win Mystery Pic twice you will be a 2x Champion instead of just a champion. The games that keep track of wins so far are Mystery Pic, <span style="font-weight: bold;">Lenny Conundrum</span> and Better Than You.</blockquote>Good news for those who want to compete for the first place.<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-584975470230141593?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-58465343050207233402001-08-14T14:01:00.000-07:002008-04-23T14:05:42.212-07:00Date released: August 14th, 2001.<br />Date rewarded: August 29th, 2001.<br /><br />This week's Conundrum is harder than the rest, and requires you to use your knowledge of Neopets :) <p> <b>To the nearest 100,000 - how many shops are there in Neopia?</b> </p> Round your answer down to the nearest hundred thousand (ie.. if you guess at 445,038 then you would say 400,000).<br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution22')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution22"><br />This week puzzle is for guessing. If you are lucky, you guess it right. The right answer is <span style="font-weight: bold;">3,000,000</span>.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-5846534305020723340?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-60554763900547298992001-08-10T16:09:00.000-07:002008-05-14T21:25:05.294-07:00Date released: August 10th, 2001.<br />Date rewarded: August 14th, 2001.<br /><br />'<i>Excuse me, Slave</i>', said Princess Vyssa, '<i>I have a job for you</i>'. '<i>What is it?</i>', Burlak groaned??? Princess Vyssa handed the sculptor a big ball of clay. '<i>I would like some decorations for my new palace. I want you to build me lots of little pyramids out of this clay. The base has to measure 8 centimeters by 8 centimeters, and they have to be 6 centimeters high.</i>. <p> </p><center> <img src="http://images.neopets.com/games/conundrum/21_clay.gif" border="0" height="150" width="150" /> </center> Burlak looked at the ball of clay, and measured it. It's diameter was 20 centimeters, and it seemed to be a perfect sphere. He wondered how many pyramids he could make... <b>do you know?</b><br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution21')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution21"><br />Volume of a pyramid [1]:<br /><div style="text-align: center;"><span style="font-style: italic;">V</span>₁ = <span style="font-style: italic;">B</span> * <span style="font-style: italic;">h</span> /3 = 8² * 6 / 3 = 128 cm³<br /></div><br />where <span style="font-style: italic;">B</span> is the area of the base of the pyramid, <span style="font-style: italic;">h</span> is the height of the pyramid.<br /><br />Volume of the sphere [2]:<br /><div style="text-align: center;"><span style="font-style: italic;">V</span>₂ = 4/3 * pi * <span style="font-style: italic;">r</span>³ = 4/3 * pi * 10³ = 4000/3 * pi cm³<br /></div><br />where <span style="font-style: italic;">r</span> is the radius of the sphere.<br /><br />Total number of pyramids that Burlak can make:<br /><div style="text-align: center;"><span style="font-style: italic;">N</span> = <span style="font-style: italic;">V</span>₂ / <span style="font-style: italic;">V</span>₁ ~ 32.72</div><br />Therefore, he can make <span style="font-weight: bold;">32</span> pyramids from the clay sphere.<br /><br /><span style="font-weight: bold;">References:</span><br />[1] <a href="http://en.wikipedia.org/wiki/Pyramid_%28geometry%29">Pyramid volume</a><br />[2] <a href="http://en.wikipedia.org/wiki/Sphere">Sphere volume</a></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-6055476390054729899?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-73395026969863431092001-08-02T21:50:00.000-07:002008-04-17T16:02:41.574-07:00Date released: August 2nd, 2001.<br />Date rewarded: August 10th, 2001.<br /><br />The economy of <b>Roo Island</b> is rather strange. They have four coins, each worth a different number of Neopoints. Three red coins plus two Neopoints equal a green coin. Three green coins plus five Neopoints equal a purple coin. Eleven red coins plus a single Neopoint equal a purple coin. <p> </p><center> <img src="http://images.neopets.com/games/conundrum/20_coin1.gif" border="0" height="80" width="80" /> <img src="http://images.neopets.com/games/conundrum/20_coin2.gif" border="0" height="80" width="80" /> <img src="http://images.neopets.com/games/conundrum/20_coin3.gif" border="0" height="80" width="80" /> </center> The fourth coin is a silver coin that is worth four purple coins. If I go to the Roo Island bakery and buy a loaf of bread worth <b>84</b> Neopoints with my silver coin, and the shopkeeper gives me change in red coins... how many red coins would I get?<br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution20')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution20"><br />Let <span style="font-style: italic;">r</span>, <span style="font-style: italic;">g</span>, <span style="font-style: italic;">p</span>, <span style="font-style: italic;">s</span> be the values of red, green, purple and silver coins respectively. We know that:<br /><br />* Three red coins plus two Neopoints equal a green coin:<br /><div style="text-align: center;">3<span style="font-style: italic;">r</span> + 2 = <span style="font-style: italic;">g</span> (1)<br /></div><br />* Three green coins plus five Neopoints equal a purple coin:<br /><div style="text-align: center;">3<span style="font-style: italic;">g</span> + 5 = <span style="font-style: italic;">p</span> (2)<br /></div><br />* Eleven red coins plus a single Neopoint equal a purple coin:<br /><div style="text-align: center;">11<span style="font-style: italic;">r</span> + 1 = <span style="font-style: italic;">p</span> (3)<br /></div><br />* Silver coin is worth four purple coins:<br /><div style="text-align: center;"><span style="font-style: italic;">s</span> = 4<span style="font-style: italic;">p</span> (4)<br /></div><br />From (2) and (3), we have:<br /><div style="text-align: center;">3<span style="font-style: italic;">g</span> + 5 = 11<span style="font-style: italic;">r</span> + 1 <=> 11<span style="font-style: italic;">r</span> = 3<span style="font-style: italic;">g</span> + 4 (5)<br /></div><br />From (1) and (5), we have:<br /><div style="text-align: center;">11<span style="font-style: italic;">r</span> = 3<span style="font-style: italic;">g</span> + 4 = 3 * (3<span style="font-style: italic;">r</span> + 2) + 4 = 9<span style="font-style: italic;">r</span> + 10 <=> 2<span style="font-style: italic;">r</span> = 10 <=> <span style="font-style: italic;">r</span> = 5<br /></div><br />Therefore:<br /><div style="text-align: center;"><span style="font-style: italic;">g</span> = 3<span style="font-style: italic;">r</span> + 2 = 17<br /><span style="font-style: italic;">p</span> = 3<span style="font-style: italic;">g</span> + 5 = 56<br /><span style="font-style: italic;">s</span> = 4<span style="font-style: italic;">p</span> = 224<br /><br /><div style="text-align: left;">The change that I should get (in red coins):<br /><div style="text-align: center;">change = (224 - 84) / 5 = 140 / 5 = 28</div><br />I should get back <span style="font-weight: bold;">28 red coins</span>.</div></div></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-7339502696986343109?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-30200952610369768952001-07-24T15:21:00.000-07:002008-04-14T15:33:36.846-07:00Date released: July 24th, 2001.<br />Date rewarded: August 2nd, 2001.<br /><br />Richard Chia is back... and he has a new anagram!!! <p> </p><center> <img src="http://images.neopets.com/games/conundrum/13_richard.gif" border="0" height="100" width="100" /> </center> <p> Hello and Welcome to the Lenny Conundrum. This weeks conundrum is a 10-letter word or phrase that has been jumbled up, can you work out what it is? </p><p> </p><center> <img src="http://images.neopets.com/games/conundrum/19_letters.gif" border="0" height="50" width="299" /><br /><br /><span style="font-weight: bold;">Prize</span><br />Unknown</center><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution19')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution19"><br />Another Richard Chia puzzle. This week answer is <span style="font-weight: bold;">Space Usuki</span>.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-3020095261036976895?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-28739969307781452922001-07-18T12:35:00.000-07:002008-04-14T13:32:37.728-07:00Date released: July 18th, 2001.<br />Date rewarded: July 24th, 2001.<br /><br />Heermeedjet the Meerca has 5,000 Neopoints in his pocket (after successfully breaking into somebody's Neohome). He has a go on the Wheel of Excitement and then increases the amount of money he has by 20%. He then takes 20% of his money and spends it on Neggs. <p> </p><center> <img src="http://images.neopets.com/pets/80by80/meerca_brown_happy.gif" border="0" height="80" width="80" /> </center> <p> Heermeedjet then puts the rest of the money in the National Neopian Bank, and earns 1% interest every day (daily interest is rounded down) for 10 days. After 10 days he gets bored and puts the all the money on a Poogle at 3:1 odds and wins.</p><br /><b>How much money does Heermeedjet have left?</b><br /><br /><div style="text-align: center;"><span style="font-weight: bold;"><b>Prize</b></span><br />Unknown</div><b><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution18')"><u>Click to show/hide solution</u></a><br /></b><div class="commenthidden" id="Solution18"><b><br /></b>Heermeedjet starts off with 5,000 NP.<br />He gains 20% through the Wheel of Excitement, so he has:<br /><div style="text-align: center;">5,000 * 120% = 6,000<br /></div><br />He spends 20% on Neggs, so he has left:<br /><div style="text-align: center;">6,000 * 80% = 4,800</div><br />He puts the NP into bank, and earn interest everyday. Here is what he earns for 10 days (interests are rounded down):<br /><ol><li>Day 1: 1% of 4,800 = 48. He then has 4,848 NPs.</li><li>Day 2: 1% of 4,848 = 48. He then has 4,896 NPs.</li><li>Day 3: 1% of 4,896 = 48. He then has 4,944 NPs.</li><li>Day 4: 1% of 4,944 = 49. He then has 4,993 NPs.</li><li>Day 5: 1% of 4,993 = 49. He then has 5,042 NPs.</li><li>Day 6: 1% of 5,042 = 50. He then has 5,092 NPs.</li><li>Day 7: 1% of 5,092 = 50. He then has 5,142 NPs.</li><li>Day 8: 1% of 5,142 = 51. He then has 5,193 NPs.</li><li>Day 9: 1% of 5,193 = 51. He then has 5,244 NPs.</li><li>Day 10: 1% of 5,244 = 52. He then has 5,296 NPs.</li></ol><br />He puts all NPs into Poogle Race with odd 3:1 and wins (hence he quadruples his NPs). So he has:<br /><div style="text-align: center;">5,296 * 4 = 21,184</div><br />Heermeedjet has <span style="font-weight: bold;">21,184 NPs</span> left.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-2873996930778145292?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-68587640366022938432001-07-10T13:37:00.000-07:002008-04-14T12:51:38.795-07:00Date released: July 10th, 2001.<br />Date rewarded: July 18th, 2001.<br /><br />Richard Chia is back... and he has a new anagram!!! <p> </p><center> <img src="http://images.neopets.com/games/conundrum/13_richard.gif" border="0" height="100" width="100" /> </center> <p> Hello and Welcome to the Lenny Conundrum. This weeks conundrum is a 10-letter word or phrase that has been jumbled up, can you work out what it is? </p><p> </p><center> <img src="http://images.neopets.com/games/conundrum/17_letters.gif" border="0" height="50" width="299" /> </center> <br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution17')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution17"><br />Another word unscrambling puzzle. The answer is <span style="font-weight: bold;">Sporkle Leg</span>.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-6858764036602293843?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-49531261890425014302001-07-06T12:44:00.000-07:002008-10-11T07:42:29.334-07:00<b></b>Date released: July 6th, 2001.<br />Date rewarded: July 10th, 2001.<br /><br />Senator Barca came rushing over the Sand Dune to talk to Peopatra. '<i>Help, Im being chased by Grundos. Can I hide here???</i>'. Peopatra nodded and lifted up the carpet concealing the trapdoor in the floor of her tent. <p> All but two of the Grundos chasing Barca were Green, all but two of the Grundos were Purple, and all but two of the Grundos were Red. </p><p> </p><center> <img src="http://images.neopets.com/pets/closeattack/grundo_troop_left.gif" border="0" width="150" height="150" /></center><br /><b>How many Grundos were chasing Barca???<br /><br /></b><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution16')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution16"><br />Let <span style="font-style: italic;">x</span> be the number of Grundo.<br />Number of Green Grundos: <span style="font-style: italic;">x</span> - 2<br />Number of Purple Grundos: <span style="font-style: italic;">x</span> -2<br />Number of Red Grundos: <span style="font-style: italic;">x</span> -2<br /><br />Therefore, number of all Grundos:<br /><div style="text-align: center;">(<span style="font-style: italic;">x</span> - 2) + (<span style="font-style: italic;">x</span> - 2) + (<span style="font-style: italic;">x</span> - 2) = <span style="font-style: italic;">x</span> <=> 3<span style="font-style: italic;">x</span> - 6 = <span style="font-style: italic;">x</span> <=> 2<span style="font-style: italic;">x</span> = 6 <=> <span style="font-style: italic;">x</span> = 3<br /></div><br />There are <span style="font-weight: bold;">3</span> Grundos. (one of each color)</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-4953126189042501430?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com2tag:blogger.com,1999:blog-774738449594515927.post-56597098536000419922001-06-27T10:27:00.000-07:002008-04-13T13:02:51.719-07:00Date released: June 27th, 2001.<br />Date rewarded: July 6th, 2001.<br /><br />Two kings of Sakhmet from history were King Galat-Ra the Lupe and King Hephaes-Ru the Kacheek. Galat-Ra died 120 years after Hephaes-Ru was born. Their combined ages when they died was 100 years. Hephaes-Ru died in the year 40 B.N. (Before Neopia). <p> </p><center> <img src="http://images.neopets.com/pets/happy/lupe_desert_baby.gif" border="0" height="150" width="150" /> </center> <b>In what year was King Galat-Ra born?</b><br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/pet_des_1.gif" /><br /><u>Geb</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution15')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution15"><br />Let <span style="font-style: italic;">x</span> be the year King Galat-Ra was born, <span style="font-style: italic;">y</span> be the year King Hephaes-Ru was born. We know that: "Galat-Ra died 120 years after Hephaes-Ru was born". Therefore, Galat-Ra died in the year <span><span style="font-style: italic;">y</span> + 120</span>. His age when he died is <span style="font-style: italic;">y </span><span>+ 120 -</span><span style="font-style: italic;"> x</span>. Hephaes-Ru's age when he died is 40 B.N. - <span style="font-style: italic;">y</span>.<br /><br />We also know that: "Their combined ages when they died was 100 years." Therefore:<br /><div style="text-align: center;"><span style="font-style: italic;">y</span> + 120 - <span style="font-style: italic;">x</span> + 40 B.N. - <span style="font-style: italic;">y</span> = 100 <=> <span style="font-style: italic;">x</span> = 40 B.N. + 20 = 20 B.N.</div><br />King Galat-Ra was born in <span style="font-weight: bold;">20 B.N.</span></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-5659709853600041992?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-3033542591082954892001-06-20T10:14:00.000-07:002008-04-13T10:50:17.527-07:00Date released: June 20th, 2001.<br />Date rewarded: June 27th, 2001.<br /><br />Once again this week Richard Chia will provide you with a confusing anagram! <p> </p><center> <img src="http://images.neopets.com/games/conundrum/13_richard.gif" border="0" height="100" width="100" /> </center> <p> Hello and Welcome to the Lenny Conundrum. This weeks conundrum is a 11-letter word that has been jumbled up, can you work out what it is? </p><p> </p><center> <img src="http://images.neopets.com/games/conundrum/14_letters.gif" border="0" height="50" width="327" /><br /><br /><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/magic_kaubottle.gif" /><br /><u>Kauvaras Potion</u></center><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution14')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution14"><br />Same type of puzzle as last week. The answer is <span style="font-weight: bold;">Tigersquash</span>.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-303354259108295489?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-2380477645634709802001-06-13T10:04:00.000-07:002008-04-13T10:51:52.593-07:00Date released: June 13th, 2001.<br />Date rewarded: June 20th, 2001.<br /><br />For this week's conundrum, I would like to pass you to my good friend Richard Chia. <p> </p><center> <img src="http://images.neopets.com/games/conundrum/13_richard.gif" border="0" height="100" width="100" /> </center> <p> Hello and Welcome to the Lenny Conundrum. This weeks conundrum is a 10-letter word that has been jumbled up, can you work out what it is? </p><p> </p><center> <img src="http://images.neopets.com/games/conundrum/13_letters.gif" border="0" height="50" width="300" /><br /><br /><span style="font-weight: bold;">Prize</span><br />Unknown</center><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution13')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution13"><br />This is unscrambling puzzle type. The answer is <span style="font-weight: bold;">Pterattack</span>.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-238047764563470980?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-3313349728946371682001-06-06T06:34:00.000-07:002008-04-13T10:51:03.783-07:00Date released: June 6th, 2001.<br />Date rewarded: June 13th, 2001.<br /><br />Mrs. Doyle the Housekeeper JubJub has made a big, big pile of sandwiches for the party of Skeiths visiting her house tonight. When she counts them, she realises that she can equally split the sandwiches between two Skeiths and have none left over. She can also split them between three Skeiths, four Skeiths, five Skeiths and six Skeiths equally and every time there will be no sandwiches left over. <p> </p><center> <img src="http://images.neopets.com/games/conundrum/12_doyle.gif" border="0" height="100" width="100" /></center><p> <b>What is the smallest amount of sandwiches that Mrs. Doyle could have made?</b></p><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution12')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution12"><br />The number of sandwiches is divisible by 2, 3, 4, 5 and 6. We want the find the least common multiple of the above numbers.<br /><div style="text-align: center;">2 = 2<br />3 = 3<br />4 = 2²<br />5 = 5<br />6 = 2 * 3<br /></div><br />The least common multiple is:<br /><div style="text-align: center;">2² * 3 * 5 = 60<br /></div><br />Therefore, the number of sandwiches is <span style="font-weight: bold;">60</span>.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-331334972894637168?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-28534312125792944292001-05-30T06:14:00.000-07:002008-04-13T10:50:46.931-07:00Date released: May 30th, 2001.<br />Date rewarded: June 6th, 2001.<br /><br /><div style="text-align: center;"><img src="http://images.neopets.com/games/cheat/5_head.gif" border="0" height="100" width="100" /> </div><p> Brucey B has just won a load of money playing Cheat! He puts 1/5 of his winnings in the National Neopian Bank, and 1/2 of his winnings he invests into shares. </p><p> After those investments Brucey realises he still has quite a lot left. He then goes to Neopia Central and spends 1/10 of his winnings on chocolate neggs! At the end of the day he goes home and puts his remaining 500 NP in his mattress.</p><br /><b>How much did Brucey B win?</b><br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution11')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution11"><br />Brucey's spending: 1/5 + 1/2 + 1/10 = 4/5. He has 1 - 4/5 = 1/5 of his winning money. That amount is 500 NPs. Therefore, his winning amount is 500 NP * 5 = <span style="font-weight: bold;">2500 NPs</span>.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-2853431212579294429?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-64071813963651312922001-05-23T22:10:00.000-07:002008-04-13T10:49:37.601-07:00Date Released: May 23rd, 2001.<br />Date Rewarded: May 30rd, 2001.<br /><br />Siya the Usuki Doll (pictured above) is 9 years older than her brother, and 25 years younger than her father. In seven years time her father will be three times older than her brother. How old is Siya now?<br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution10')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution10"><br />Let <span style="font-style: italic;">x</span> be Siya's age, <span style="font-style: italic;">y</span> be her brother's age and <span style="font-style: italic;">z</span> be her father's age. We know:<br /><div style="text-align: center;"><span style="font-style: italic;">y</span> = <span style="font-style: italic;">x</span> - 9<br /><span style="font-style: italic;">z</span> = <span style="font-style: italic;">x</span> + 25<br /></div><br />In seven years, her brother's age and her father's age will be <span style="font-style: italic;">x</span> - <span style="font-style: italic;">2</span> and <span style="font-style: italic;">x</span> + 32 respectively (add 7 to <span style="font-style: italic;">y</span> and <span style="font-style: italic;">z</span>). Her father's age will be three times her brother's age then. Therefore,<br /><div style="text-align: center;"><span style="font-style: italic;">x</span> + 32 = 3 * (<span style="font-style: italic;">x</span> - 2) <=> <span style="font-style: italic;">x</span> + 32 = 3<span style="font-style: italic;">x</span> - 6 <=> 2<span style="font-style: italic;">x</span> = 38 <=> <span style="font-style: italic;">x</span> = 19<br /></div><br />Therefore, Siya is <span style="font-weight: bold;">19</span> years old now.<br /><br /><u>Check</u>: her brother's age = 10, her father's age = 44. In seven years, her father's age = 51, three times as much as her brother's age = 17.<br /></div><br /><u>Note</u>: The picture is missing.<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-6407181396365131292?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-33914020046380516792001-05-15T15:14:00.000-07:002008-04-13T10:48:16.780-07:00Date Released: May 15th, 2001.<br />Date Rewarded: May 23rd, 2001.<br /><br />There are six Moehogs travelling to Neopia Central, and each Moehog is carrying six baskets. In each basket are six Puppyblews, and each Puppyblew has had two baby Puppyblews. How many legs are there in total between all the Moehogs and Puppyblews?<br /><br /><center><img src="http://images.neopets.com/pets/happy/moehog_yellow_baby.gif" border="0" height="150" width="150" /><img src="http://images.neopets.com/items/pets_blew.gif" border="0" height="80" width="80" /></center><br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution9')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution9"><br />Number of Moehogs: 6.<br />Number of baskets: 6 x 6 = 36.<br />Number of Puppyblews: 36 x 6 = 216.<br />Number of baby Puppyblews: 216 x 2 = 432.<br /><br />Number of legs: (6 + 216 + 432) x 4 = 2616. The answer is: there are <span style="font-weight: bold;">2616</span> legs.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-3391402004638051679?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-74138961828173836462001-05-08T17:25:00.000-07:002008-10-13T12:04:11.910-07:00Date Released: May 8th, 2001.<br />Date Rewarded: May 15th, 2001.<br /><br />What's the next letter in the following sequence?<br /><br /><b>W T N L I T F _ ?</b><br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br /><br /><img src="http://images.neopets.com/items/shadowpntbrsh.gif" /><br /><u>Shadow Paint Brush</u></div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution8')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution8"><br />Each letter in the sequence is the first letter of each word in the question. Therefore, the answer is <span style="font-weight: bold;">S</span>.</div><br /><u>Note:</u> The prize used to be named Shadowed Paint Brush.<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-7413896182817383646?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-80271362899291439452001-05-01T14:07:00.000-07:002008-04-10T17:35:23.078-07:00Date Released: May 1st, 2001.<br />Date Rewarded: May 8th, 2001.<br /><b><br />How many letters are in the answer to this question?</b><span style="font-weight: bold;"><br /><br /></span><b>HINT</b> : Don't bother counting the letters in the phrase 'the answer to this question' - we already thought of that, and its the incorrect answer!<br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution7')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution7"><br />The answer of this question must be a number (in either digit or alphabetical form). If it is in the digit form, it does not have any letters. Therefore, the correct answer is 0. If it is in the alphabetical form, only one number satisfies this condition (four = 4). Therefore, the answer should be <span style="font-weight: bold;">0</span> or <span style="font-weight: bold;">four</span>.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-8027136289929143945?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-82838305329060939922001-04-25T16:37:00.000-07:002009-02-26T08:55:03.065-08:00<b></b>Date Released: April 25th, 2001.<br />Date Rewarded: May 1st, 2001.<br /><br /><center> <img src="http://images.neopets.com/games/conundrum/confused3.gif" border="0" width="150" height="150" /><br /><br /></center> If you wrote all of the numbers from <b>300</b> to <b>400</b> on a piece of paper, how many times would you have written the number 3?<br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution6')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution6"><br />There are 100 numbers from 300 to 399. Each one has a number 3 in the 1st digit. (hundreds place)<br />There are 10 numbers from 330 to 339. Each one has a number 3 in the 2nd digit. (tens place)<br />There are 10 numbers that has a number 3 in the last digit (ones place) i.e. 303, 313, 323 ... 393.<br /><br />Therefore, there are totally <span style="font-weight: bold;">120</span> times of number 3 from number 300 to number 400.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-8283830532906093992?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-35814852032041081992001-04-19T16:23:00.000-07:002008-04-10T17:36:40.175-07:00Date Released: April 19th, 2001.<br />Date Rewarded: April 25th, 2001<br /><br />The total number of Neopoints worth of goods bought every day in Neopia is <b>8,549,176,320 NP</b>. What is special about that number?<br /><br /><div style="text-align: center;"><b>Prize</b><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution5')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution5"><br /><span style="font-weight: bold;">All the digits in the number are in alphabetical order</span>: Eight, Five, Four, Nine, One, Seven, Six, Three, Two, Zero.<br /><span class="content"></span></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-3581485203204108199?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-10857586475599438902001-04-10T15:17:00.000-07:002008-04-10T17:37:43.242-07:00Date Released: April 10th, 2001.<br />Date Rewarded: April 19th, 2001.<br /><br /><div style="text-align: left;"></div><center><div style="text-align: left;">This weeks conundrum is less confusing than last weeks... but it's still quite tricky.<br /></div><p style="text-align: left;">My question is : <b>What are the next two letters in this series: A E F H I K L M ?</b></p><center><br /><img src="http://images.neopets.com/pets/80by80/chomby_red_sad.gif" border="0" height="80" width="80" /><br /><br /><b>It's too hard!!!<br /><br /></b><b>Prize<br /></b>Unknown</center></center><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution4')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution4"><br />Those letter are made of straight lines only. Other letters between the above letters: B, C, D, G, J having curves in them. Therefore, the next two letters are <span style="font-weight: bold;">N</span> and <span style="font-weight: bold;">T</span>.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-1085758647559943890?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-51789393597882817572001-04-03T09:20:00.000-07:002008-10-09T21:12:56.970-07:00Date Released: April 3rd, 2001.<br />Date Rewarded: April 10th, 2001.<br /><br /><center><div style="text-align: left;"><i>I spent one third of my life in school,</i><br /><i>I spent four years working in a bakery in Neopia Central,</i><br /><i>I spent the next three years smuggling Juppies in Mystery Island.</i><br /></div><br /><div style="text-align: left;"><b>How old am I?</b><br /></div><b><br />Prize<br /></b>Unknown</center><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution3')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution3"><br />According to the news, "The correct answer to last week's was <i style="font-weight: bold;">Thirty-Four</i> as it was in fact referring to Mulvinn the Wocky." TNT took it down and replaced with "The Nightsteed" article.<br /><br /><u>Note</u>: If you have a copy of that article, please let me know.</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-5178939359788281757?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-59064097478494384872001-03-27T07:16:00.000-08:002009-02-26T08:20:48.505-08:00Date released: March 27th, 2001.<br />Date rewarded: April 3rd, 2001.<br /><br /><p> </p><center><img src="http://images.neopets.com/pets/angry/skeith_red_baby.gif" border="0" width="150" height="150" /><br /></center>A Skeith weighs 100 pounds plus half of his weight. How much does he weigh?<br /><br /><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution2')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution2"><br />Let <span style="font-style: italic;">x</span> be the weight of the Skeith. We have:<br /><div style="text-align: center;"><span style="font-style: italic;">x</span> = 100 + 0.5<span style="font-style: italic;">x</span> <=> 0.5<span style="font-style: italic;">x</span> = 100 <=> <span style="font-style: italic;">x</span> = 200<br /><br /><div style="text-align: left;">Another way to look at the puzzle is: the skeith weighs 100 pounds plus half of his weight. Therefore, 100 pounds must be the other half of his weight. Then, his weight is 200 pounds.<br /><br />Therefore, the Skeith weighs <span style="font-weight: bold;">200</span> pounds.<br /></div></div></div><br /><u>Note</u>: the game has the trophies.<br /><br /><div style="text-align: center;"><img src="http://images.neopets.com/trophies/106_1.gif" /><img src="http://images.neopets.com/trophies/106_2.gif" /><img src="http://images.neopets.com/trophies/106_3.gif" /></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-5906409747849438487?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0tag:blogger.com,1999:blog-774738449594515927.post-4675455859039779542001-03-23T22:17:00.000-08:002008-04-10T17:41:20.544-07:00Date released: March 23rd, 2001.<br />Date rewarded: March 27th, 2001.<br /><br /><div style="text-align: center;"><img src="http://images.neopets.com/pets/80by80/nimmo_blue_happy.gif" border="0" height="80" width="80" /><img src="http://images.neopets.com/pets/80by80/nimmo_green_happy.gif" border="0" height="80" width="80" /></div><br />There are two Nimmos. The blue Nimmo points to the green one and says...<br /><i><br />Brothers and sisters I have none,<br />But this Nimmo's father is my father's son...<br /></i><br /><b>My question is... What relation is the blue one to the green one?<br /><br /></b><div style="text-align: center;"><span style="font-weight: bold;">Prize</span><br />Unknown</div><br /><a aiotitle="Click to expand" href="javascript:togglecomments('Solution1')"><u>Click to show/hide solution</u></a><br /><div class="commenthidden" id="Solution1"><br />Let B - Blue Nimmo, G - Green Nimmo. B said: G's father = B's father's son. Since B does not have any brothers and sisters, he is the only son of his father. So B's father's son = B.<br /><br />We then have G's father = B's father's son = B. Therefore, B is G's father. The answer should be: <span style="font-weight: bold;">the Blue Nimmo is the father of the Green Nimmo</span>.<br /></div><br /><u>Note</u>: This is the first Lenny Conundrum ever. According to the news: "The first <b>1000</b> people to answer the riddle correctly will get a unique prize". The old Lenny Conundrum pose is below.<br /><br /><div style="text-align: center;"><img src="http://images.neopets.com/games/lennywizard.gif" border="0" height="150" width="150" /></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/774738449594515927-467545585903977954?l=lennyconundrumsolutions.blogspot.com' alt='' /></div>LC Solverhttp://www.blogger.com/profile/18073289329448713412noreply@blogger.com0