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?
For the first logician to know the word, his letter must have been either H, R, P, D, V, because each letter is only used once. From this, the other two logicians must have know that the word was either Hoe, Oar, Pad or Vat.
For the second logician to know the word, hemust have had and E, T or P/D (whichever the first didn't have). This means that the word was either HOE, PAD or VAT.
Out of them, the third logician must have the middle letter of whatever the word is, because the first two logicians had the other two. Because he knew the word, this means that he must have had an O and the word was HOE.
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Posted by Lewis
on 2003-06-19 11:03:07 |
Solution
