Round 304

we 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...

Reviving the blog

Today, 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.

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).

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.

LC Solver

Round 303

Date Released: March 19th, 2009.
Date Rewarded: March 26th, 2009. (estimated)

Rearrange the letters in the following phrase to come up with a Neopian word or phrase:

ROTATE SOON VIA RAIL

Submit only the answer with no other information, otherwise your answer will be marked as incorrect!

Prize

Steam Train Gummies

Click to show/hide hint

It is related to a character in the current Daily Dare event: Aristotle A Avinroo.

Round 302

Date Released: March 12th, 2009.
Date Rewarded: March 17th, 2009.

271 - 482 = 436

148 + 591 = 866

4881 + 8914 = 6562

8827 * 1178 = ?

Do NOT show your work; submit only a single number, with no punctuation, as your answer.

Prize


Rotawheel

Click to show/hide solution

To be easy to work on this problem, we convert all the digits into alphabetical letters in the following scheme: a = 1, b = 2, c = 3, d = 4, e = 5, f = 6, g = 7, h = 8, i = 9. Then we have three equations:

bga = dhb + dcf (1)
adh + eia = hff (2)
dhha + hiad = fefb (3)

Before we solve the problem, we have to assume that each letter represent a unique digit (distinct property.) For example, if a is 4, then b must not be 4. Also, all the digits in the hundreds' places in (1) and (2) and thousands' places in (3) must not be 0.

If we look at the equation (1) at the hundreds' place, we have b = d + d. So, we know that 1 <= d <= 4 because d can't be 0 and if d >= 5 then b is not a digit. There are four cases:

• d = 1: b can be either 2 or 3 (in the case of carry from the tens' place.)
• d = 2: b can be either 4 or 5.
• d = 3: b can be either 6 or 7.
• d = 4: b can be either 8 or 9.

If we look at the equation (3) at the unit's place, we have a + d = b. Then, the four cases will be following:

• d = 1: b = 2 => a = 1 (violate the distinct property), b = 3 => a = 2
  
• d = 2: b = 4 => a = 2 (violate the distinct property), b = 5 => a = 3
• d = 3: b = 6 => a = 3 (violate the distinct property), b = 7 => a = 4
• d = 4: b = 8 => a = 4 (violate the distinct property), b = 9 => a = 5

If we look at the equation (1) at the unit's place, we have a = b + f. Then, the four cases will be following:

• d = 1: a = 2, b = 3 => f = 9
• d = 2: a = 3, b = 5 => f = 8
• d = 3: a = 4, b = 7 => f = 7 (violate the distinct property)
• d = 4: a = 5, b = 9 => f = 6

There are only three cases left after the last analysis. If we look at the equation (2) at the unit's place, we have h + a = f. Then, the three cases will be following:

• d = 1: b = 3, f = 9, a = 2 => h = 7
  
• d = 2: b = 5, f = 8, a = 3 => h = 5 (violate the distinct property)
• d = 4: b = 9, f = 6, a = 5 => h = 1

There are only two cases left now. However, if we look at the equation (2) at the hundreds' place, we have a + e = h. In the last case, a = 5 and h = 1. It is impossible to get since h > a. Therefore, only the first case is correct. Then, we have: a = 2, b = 3, d = 1, f = 9, h = 7

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: d + i = f <=> i = f - d = 9 - 1 = 8 (no carry either). Then, we look at the same equation at the hundreds' place, we can write: a + e = h <=> e = h - a = 7 - 2 = 5.

Then, we look at the equation (1) at the tens' place. Since there is a carry on the unit's place (a = 2 = 3 + 9 = b + f), we can write: g = h + c + 1 <=> g = c + 8. Since 1, 2, 3, 5, 7, 8, 9 are already taken. c and g can only be 0, 4 or 6. Only the pair c = 6 and g = 4 are satisfied this equation. Therefore, we have: a = 2, b = 3, c = 6, d = 1, e = 5, f = 9, g = 4, h = 7, i = 8.

Round 301

I 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...

Round 292

I'm not online New Year Eve. If this round comes out soon, feel free to discuss. I will update later. Happy New Year :)

Round 291

Check the Hidden Tower

http://www.neopets.com/faerieland/hiddentower938.phtml

Use the second letter of each item to get the question and check the Hidden Tower for the answer. Good luck!

Round 290

Thanks for all the comments. Look like it is a good answer

Advent Calendar NP rewards:

Day 1: 324 NPs
Day 2: 945 NPs
Day 3: 394 NPs
Total: 324 + 945 + 394 = 1663 NPs

Day 4: 295 NPs
Day 5: 953 NPs
Day 6: 279 NPs
Total: 295 + 953 + 279 = 1527 NPs

Day 7: 273 NPs
Day 8: 479 NPs
Day 9: 374 NPs
Total: 273 + 479 + 374 = 1126 NPs

Day 10: 179 NPs
Day 11: 278 NPs
Day 12: 639 NPs
Total: 179 + 278 + 639 = 1096 NPs

Day 13: 730 NPs
Day 14: 579 NPs
Day 15: ? NPs
Total: 730 + 579 + ? = 1309 + ? = ? NPs

Good luck :)

Next round

Crosses all the worlds, we get the below:




The question is read backwards from the remaining letters:

"what is the numeric deactivation code for the evil program dr sloth created?"

Check step 24 of the below link

http://www.neopets.com/space/npv2_solution.phtml

(Please submit the answer with no spaces or punctuation)

Round 288

Ra
Shah
Roo
Ee

http://www.neopets.com/pronounce.phtml

check out the first four pets then you know the next one... :)

Round 287

I think this may be the final version.

Tier 1: r1 = d1/2 = 6 in (bottom)
Tier 2: r2 = d2/2 = 5.25 in (middle)
Tier 3: r3 = d3/2 = 4.5 in (top)
Height: h = 1.5 in (height of a layer)

V(cake) = pi * ((r1-1/3)^2 + (r2-1/3)^2 + (r3-1/3)^2) * (3*h)

V(frost_side) = pi * (2/3 r1 + 2/3 r2 + 2/3 r3 - 1/3) * (3*h+1/2)
V(frost_top) = pi * (r1^2 + r2^2 + r3^2) * 1/3
V(frost) = V(frost_top) + V(frost_side)

V(jam) = pi * ((r1 - 1/3)^2 + (r2 - 1/3)^2 + (r3 - 1/3)^2) * 1/2

weight = V(cake) * 0.35 + V(frost) * 0.48 + V(jam) * 0.6

cal = weight * 53.4

Remember not to round before the the final answer. Good luck.

Round 286

This 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)

Your choice of submission

Round 285

This is the total points for each Neopet. Look like they are matched with the comments (at least one of them)


Acara: 7
Aisha: 7
Blumaroo: 19
Bori: 12
Bruce: 7
Buzz: 10
Chia: 13
Chomby: 39
Cybunny: 11
Draik: 55
Elephante: 42
Eyrie: 22
Flotsam: 8
Gelert: 18
Gnorbu: 8
Grarrl: 9
Grundo: 9
Hissi: -1
Ixi: 21
Jetsam: 5
JubJub: 12
Kacheek: 15
Kau: 5
Kiko: 13
Korbat: 9
Kougra: 7
Krawk: 6
Kyrii: -2
Lenny: 9
Lupe: 11
Lutari: 3
Meerca: 15
Moehog: 13
Mynci: 35
Nimmo: 19
Orgin: 20
Peophin: 20
Poogle: 19
Pteri: 3
Quiggle: 18
Ruki: 8
Scorchio: 25
Shoyru: 10
Skeith: 12
Techo: 13
Tonu: 13
Tuskanniny: 26
Uni: 13
Usul: 23
Wocky: 11
Xweetok: 31
Yurble: 13
Zafara: 1

Round 284

Use the base converter below for conversion

http://www.mste.uiuc.edu/users/exner/ncsa/base/

I found that the following is match:
553 (base 13)
546 (base 23)
897 (base 17)
318 (base 19)

converts all 4 numbers into base 10 and sum them up then convert back to the base 32 and submit the answer.

This is where you can learn about base:
http://en.wikipedia.org/wiki/Base_(mathematics)

Round 283

What do you get when you multiply six by nine?

If there is no tricks, you shouldn't need hints? or would you... ?

Some people suggest this one:

http://en.wikipedia.org/wiki/Answer_to_life_the_universe_and_everything#Arthur.27s_Scrabble_tiles

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...

Round 282

Date Released: October 9th, 2008.
Date Rewarded: October 16th, 2008.

As you may know, each Neopets item has a numerical rarity associated with it. So add up the following:

The rarity of the item awarded in Lenny Conundrum #92
+ The rarity of the item awarded in Lenny Conundrum #107
+ The rarity of the item awarded in Lenny Conundrum #129
+ The rarity of the item awarded in Lenny Conundrum #142
+ The rarity of the item awarded in Lenny Conundrum #192
+ The rarity of the item awarded in Lenny Conundrum #219
+ The rarity of the item awarded in Lenny Conundrum #229
+ The rarity of the item awarded in Lenny Conundrum #281

What is the total? If a rarity has changed since the prize was first awarded, go with the current rarity. And please, submit only a number with no punctuation or other information.

Prize


Autumn Leaf Wreath

Click to show/hide hints

The prize for each round and its rarity are below:

Round 92 - Happy Birthday Negg (rarity 89)
Round 107 - Filamen (rarity 89)
Round 129 - Ice Scimitar (rarity 87)
Round 142 - Baby Rattle (rarity 92)
Round 192 - Large Chia Cake (rarity 90)
Round 219 - Wartroot Snorkle Lollypop (rarity 82)
Round 229 - Quill and Ink (rarity 91)
Round 281 - Grandfather clock (rarity 90)

Note: Brain Tree Mace is not a correct prize for round 107.

The answer is the sum of all rarity numbers.

Round 281

Date Released: October 2nd, 2008.
Date Rewarded: October 9th, 2008.

Walking into Chesterdrawer's Antiques, 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.

What should the fourth clock read?

Prize


Grandfather Clock

Click to show/hide solution

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.

A	B	C	D	E	F
G	H	I	J	K	L
M	N	O	P	Q	R
S	T	U	V	W	X
Y	Z

9:00 => P
6:07 => E
10:45 => O
(the 4th clock)
7:45 => H
7:52 =>I
4:37 => N

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 9:00.

Results: 1885 people guessed the correct answer earning themselves 1062 NP each.

References:
[1] Flag Semaphore Characters

Round 280

Date Released: September 25th, 2008.
Date Rewarded: October 2nd, 2008.

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.

Suppose a₁ is the first digit (after the decimal point) of Pi, a₂ is the second digit, and so on...

What would the following formula equal:

(a₁ - a₂) * (a₂ - a₃) * (a₃ - a₄) * ... * (a₉₉ - a₁₀₀)

What is the answer?

Prize


Flatfruit Table

Click to show/hide hints

The numerical value of PI truncated to 100 decimal places [1] is:

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679

We notice that a₂₄ = a₂₅ = 3. Therefore the formula equal to:

(a₁ - a₂) * (a₂ - a₃) * ... * (a₂₃ - a₂₄) * 0 * (a₂₅ - a₂₆) * ... * (a₉₉ - a₁₀₀) = 0

There are several other pairs of consecutive digits that are the same. The answer is 0.

Results: 6249 people guessed the correct answer earning themselves 321 NP each.

References:
[1] Decimal expansion of PI

Round 279

Date Released: September 18th, 2008.
Date Rewarded: September 25th, 2008.

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.

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:

1 : G
2 : A if preceded by an odd digit, P if preceded by an even digit
3 : H if preceded by an odd digit, R if preceded by an even digit
4 : T if preceded by an odd digit, Y if preceded by an even digit
5 : O if preceded by an odd digit, E if preceded by an even digit.
6 : N
7 : D
8 : U if preceded by an odd digit, I if preceded by an even digit.
9 : S if preceded by an odd digit, W if preceded by an even digit.
0 : L if preceded by an odd digit, M if preceded by an even digit.

Then, unscramble these letters to find a Neopian word. What is the word? Please only submit a single word, with no other information or punctuation, or your answer may be disqualified.

Prize


Rainbow Arm Chair

Click to show/hide solution

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 Round 269 (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.

Using 17,152,716,592 to decode, we get GDGOADGNESA. It is not supposed to be what TNT intended. It should be GDGAADGMESA or GDGMADGAESA. With either one of them, the answer is gadgadsgame. Here is what TNT said:

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.

Results: 1325 people guessed the correct answer earning themselves 1510 NP each.

Round 278

Date Released: September 11th, 2008.
Date Rewarded: September 18th, 2008.

What percentage of users answering this question will get it correct?

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.

Prize


Funky Blue and Orange Sofa

Click to show/hide solution

Another guessing game. Last week answer is 3 so a lot of people went with 3. Here is the solution from TNT

19,427 users entered this week's Lenny Conundrum. Here were the top twelve answers, with the rounded percentage of users answering each one:

1. "3" (2517 guesses, 13.0% of total entries)
2. "5" (1498 guesses, 7.7% of total entries)
3. "4" (1429 guesses, 7.4% of total entries)
4. "100" (1258 guesses, 6.5% of total entries)
5. "2" (1244 guesses, 6.4% of total entries)
6. "1" (924 guesses, 4.8% of total entries)
7. "6" (505 guesses, 2.6% of total entries)
8. "7" (444 guesses, 2.3% of total entries)
9. "50" (431 guesses, 2.2% of total entries)
10. "0" (418 guesses, 2.2% of total entries
11. "10" (402 guesses, 2.1% of total entries
12. "8" (226 guesses, 1.2% of total entries

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.

Results: 418 people guessed the correct answer earning themselves 4785 NP each.