Wednesday, August 25, 2010

1000 Bottles of Wine

Borrowed from
You are the ruler of a medieval empire and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You've got 1000 bottles of wine you were planning to open for the celebration, but you find out that one of them is poisoned.
The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison.

You have over a thousand paid caterers to help with the testing and just under 24 hours to determine which single bottle is poisoned.

You have a handful of prisoners about to be executed, and it would mar your celebration to have anyone else killed.

What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?

Wednesday, August 18, 2010


One time in college I emailed my dad asking for money and he said I could have some if I solved the following equation:


Each letter represents its own digit (0-9) and multiple occurrences of the same letter represent the same digit (eg if one of the E's represents a 3, they all do).

Friday, August 13, 2010

A Boat in a Tank

Imagine you are in a small rowboat floating in a swimming pool.  There's a big rock in the boat and you drop it overboard. Does the water level rise or fall?  Why?

Wednesday, August 4, 2010

The Magic Square

This is one I come back to when I'm bored and all I have is pen and paper.  I also read in a biography of Benjamin Franklin that he used to do this when he was stuck in boring meetings.  Construct a 3x3 grid of numbers, using numbers 1 through 9, and arrange the numbers in the square such that every row, column, and diagonal (diagonals through the center) adds up to 15. 

Too easy?  Now construct a 4x4 grid made out of numbers 1 through 16, such that every row, column, and diagonal adds up to 34.  This one is killing me because I figured it out once, but can't seem to rediscover the solution.  There are ways to do this for grids 5x5, 6x6, and up, though they no doubt get very difficult.