A list of eighteen three-letter words is written on a chalkboard. The logic professor hands each of his three ace students a small piece of paper and announces: “I have selected one of the words written on the board and have given each of you a different letter of that word. Without revealing your letter to your fellows, can you deduce the selected word?”
(Each of the students has displayed flawless reasoning to date and each expects that the same will be true for this challenge.)
The professor waits several moments for the students to consider the list and then begins to ask each one in turn if they have deduced the selected word pausing for several moments between each query.
Each student in turn answers “No”.
The professor waits a few minutes more and in the same order as before asks each student a second time (again pausing after each response) and again each student answers “No”.
The professor waits for several more minutes and for the third time asks each student as before if they have deduced the selected word. This time each student in turn answers “Yes”.
What is the selected word, and which letter does each student have?
ANT APE ASP AUK BAT BOA CAT DOG EMU
FLY FOX GNU JAY OWL PIG RAT RAY YAK
- In tribute to Raymond Smullyan -