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 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.