Thursday, April 24, 2008

Round 259

Date Released: April 24th, 2008.
Date Rewarded: May 1st, 2008.

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.


Speak Tyrannian

Click to show/hide solution

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 30.

Results: 4335 people guessed the correct answer earning themselves 462 NP each.

Thursday, April 17, 2008

Round 258

Date Released: April 17th, 2008.
Date Rewarded: April 24th, 2008.

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.

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)


Underwater Tour

Click to show/hide solution

First off, we need to find the maximum height of the water tank that the drain can handle using hydrostatic pressure equation [1]:
P = rho * g * h <=> h = P / (rho * g) = 5.096839959225281 m

where P = 50k Pa = 50,000 kg/m·s2 is the maximum hydrostatic pressure, rho = 1000 kg/m3 is density of water, g = 9.81 m/s2 is the gravitational acceleration. Remember that do not round h yet.

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):
V = 1000 * pi * h2 * (r - h/3) = 212276.11

where r = d/2 = 4.3 m, is the radius of the spherical water tank, h is the above maximum height.

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 V = 212,280 liters.

Results: 462 people guessed the correct answer earning themselves 4330 NP each.

If you are interested to see how the partial volume of a sphere is derived, you can continue to read. Otherwise stop here.

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 x:
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 -r to h-r

[1] Hydrostatic pressure
[2] Pythagorean theorem

Thursday, April 10, 2008

Round 257

Date Released: April 10th, 2008.
Date Rewarded: April 17th, 2008.

Figure out how to unscramble these tiles to discover this week's Lenny Conundrum


Zeenana Crepe

Click to show/hide solution

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 Zafara.

Results: 2272 people guessed the correct answer earning themselves 881 NP each.

Tuesday, April 1, 2008

About us

Every 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.

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