Here is a list of words:
(i) Each of the three logicians was told one letter of a certain word, so that each logician knew only one of the letters and so that no two logicians knew the same letter.
(ii) The logicians were then told their three letters could be arranged to spell one of the words in the list above.
(iii) When each logician was asked in turn, “Do you know which word the letters spell?,” the first logician answered, “Yes,” then the second logician answered, “Yes,” and then the third logician answered, “Yes”.
Which word did the letters spell?
I disagree with Mike's answer: the word is HOE.
The first logician had an H, so he knew the word. The second had an E, so initially he didn't know if the word was HOE or TOE. The first logician's answer solved this for him: T and O appear in more than one word, so the first must have the H from HOE.
The third has an O. Following the above logic, he knows the word isn't TOE. The only other O is in OAR. This would require the first logician having an R, and the second an A: but if that were the case, the A holder couldn't be sure it wasn't VAT, with the first holding a V. So, only HOE is left. This logic doesn't hold for any other combination.
different answer
