Friday Puzzler -- 6 words
Alex Y
A logic professor writes the following six words on the board:
Cat
Dim
Dog
Has
Max
Tag
The professor says he has picked a target word and written one letter of the word on each of three sheets of paper, and he hands out these sheets to his three best students. They are told that they may not show or tell their letters to be each other, but should announce when they have figured out the target word.
After a while, Ann says "I know the word"
A little later, Bob says "I couldn't determine the word at first, but now I have it"
Finally, Carol says "that was unfair; there was no way I could determine the word before Ann and Bob did. But now I know what it is as well"
What was the secret word?