Here is a list of words:

• HOE
• OAR
• PAD
• TOE
• VAT

(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?