Saturday, October 27, 2007

Aristotle's Number Puzzle

Archimedes, Boole, and Chebyshev, three perfectly wise thinkers, each has a hat on his head, on which is written some positive integer. The host then announces that the number on one of the hats is the sum of the numbers on the other two hats. The following statements are made:

1. Aristotle: I cannot determine my number.
2. Boole: I still cannot determine my number.
3. Chebyshev: I also still cannot determine my number.
4. Aristotle: My number is 50.

Aristotle is correct. From this fact, and from the four remarks, can you determine how Aristotle determined his number, and what the numbers on the other two hats were?
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