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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7 Responses

  1. Anonymous says:

    is it 13 and 17

  2. deepak says:

    no solution is possible coz data is insufficient and both conditions are of different domain.

  3. deepak says:

    no sol possible since data is insufficient. coz both the condition are of different domain.

  4. Rency says:

    Aristotle is not in the party…

  5. Anonymous says:

    from a dumbjarheadinMD:) the other two numbers are 1 and 49. WLOG(without loss of generality) lets say boole had 1 and chebyshev had 49. Because no two positive integers can add up to 1 then both aristotle and chebyshev realized that it was between both of them that had the integer which was the sum of the other two because the sum of their numbers would not add up to 1(boole's number). at this time aristotle didnt know if he also had a 1 on his hat so he was unable to answer. by chebyshev answering that he to was unable to answer then that confirmed to aristotle that his number was not a 1 because if it was then by chebyshev seeing that both aristotle and boole both had ones he would have known that his number was 2. since chebyshev repled that he also didnt know then that confirmed that aristotle did not have a 1 so therefore he had the sum of the other boole's and chebyshev's numbers,50

  6. Anonymous says:

    Awesome logic!!!!

  7. Anonymous says:

    13 and 17 don't add up to 50?!

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