My (faulty) thinking went this way:
If the secret word was cat, the person with the c would hand ln his paper right away, knowing that cat was the answer. Same for the person with the x if max was the secret word. But the next person (holding t for cat, or m for max) would not be able to distinguish between cat and tag or max and dim (this is before tag is eliminated). Similar argument for dog and dim at first.
So my initial thought was to eliminate cat and max, and dog and dim, leaving has and tag. My answer could have been has, but because I read (too much into) the wording of the problem that implied some time before the the first and then the second persons turned in their answers, I concluded tag had to be the answer.
So what is the correct way to think about this?