Round 272

Date Released: July 24th, 2008.
Date Rewarded: July 31st, 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 you have four numbered tiles, one with a 3 on it, one with a 4, one with a 5, and one with a 6.

What is the largest four-digit number that can be formed by these tiles that is not evenly divisible by 9? Only submit a four-digit number as your answer; any other information may disqualify your entry.

Prize


Faerie Tales: Cloud Nine

Click to show/solution

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.

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 9543.

Results: some (5503-5517) people guessed the correct answer earning themselves 363 NP each.

References:
[1] Divisibility rule

Round 271

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

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?

Please submit your answer in kilometres, and round to the nearest kilometre. Submit only a number; any additional information may disqualify your entry.

Prize


Kreludan Defender Plushie

Click to show/hide solution

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:

r³ = G*M / ω²

where r is the distance between the Neopia's center of mass to the Kreludor moon's geostationary orbit, G = 6.674 28 * 10^-11 m³/(kg*s²) is the gravitational constant, M is the mass of the Neopia and ω is the angular speed of the moon.

The mass of the Neopia planet can be calculated by the following equation:

M = ρ * V = ρ * 4/3 * pi * R³

where ρ = 5200 kg/m³ is the density of Neopia, V is the volume of the planet, R = d/2 = 800 km = 800,000 m is the radius of the planet.

The angular speed of the Kredulor moon can be calculated by the following equation:

ω = (2 * pi) / 1 sidereal day = (2 * pi) / (24 * 60 * 60) = pi/43200 rad/s

Therefore, we have:

r³ = G * ρ * 4/3 * pi * R³ / (pi/43200)² = (86400)² * G * ρ * R³ / (3*pi)

Replace numbers into the above equation, then take cubic root, we can get r = 5201692.7355. The answer is the distance from the Neopia planet surface to the orbit. Therefore, it should be:

distance = (r - R)/1000 = 4401.69

We use 1000 factor in the above equation because we want to get in kilometers. Round the distance and we get 4402 as the answer.

Results: 526 people guessed the correct answer earning themselves 3803 NP each.

References:
[1] Geostationary orbit

Round 270

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

The Monoceraptor was walking down a path one day when a Babaa appeared in front of it at exactly 8:06 AM.

The next day, the Monoceraptor was walking down the same path, and the Babaa appeared in front of it at 6:03 PM.

The next day, the same thing happened at 11:05 AM.

The next three days were at 3:09 PM, 5:05 AM, and 4:01 AM.

What time did the Babaa appear in front of the Monoceraptor on the seventh day? 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 9:15 PM. Do not include any extra information other than your answer.

Prize


Grandfather Clock

Click to show/hide solution

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.

If we write twenty four hours in words and arrange in alphabetical order, it should be: eight (8 AM), eighteen (6 PM), eleven (11 AM), fifteen (3 PM), five (5 AM), four (4 AM), 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.

For the minutes, notice the PI number: 3.14159265358979323846... The 8th digit is 6, the 18th digit is 3, the 11th digit is 5, the 15th digit is 9, the 5th digit is 5 and the 4th digit is 1. Therefore, the next minute should be corresponding to the 14th digit which is 7.

The answer is 2:07 PM.

Results: 50 people guessed the correct answer earning themselves 40,000 NP each.

Round 269

Date Released: July 3rd, 2008.
Date Rewarded: July 10th, 2008.

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.

Another ancient tomb in the Lost Desert has the following grid engraved on the tomb door:

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.

What number will you get when you multiply the circled digits? Please submit only a single number as your answer; do not submit ANY information other than the answer. Otherwise, your submission may be disqualified.

Prize


Babaa Lamp

Click to show/hide solution

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.

If we correct the red number 17 by number 4, then we can solve the grid as following:


There are two choices for the numbers that marked with 'X'


If you multiply the numbers in orange color blocks:

answer = 1 * 2² * 3⁵ * 4² * 5³ * 6 * 7 * 8 * 9² = 52907904000

Results: 1536 people guessed the correct answer earning themselves 1303 NP each.

References:
[1] Kakuro