I contend that either cat or dog could be the right answer, although the site where I saw this claimed dog was THE answer. Here is my thinking:
One person has a letter that allows him to determine the word initially. The possibilities are
The capital letters are the ones the first person may have had.
The second person realizes that those are the only possibilities that could have led to the first person's answer, and looks for frequency=1 letters in the remaining list.
It is easy to eliminate "max" and "dim", since they have no f=1 letters other than the ones the first student had.
I contend (and differ from the other solution here) that we can also eliminate "has" as a possible word for the send person. The other solution suggests that student #2 could have had whichever of h or s that student #1 did not have. But wouldn't she then have known that word initially, and handed in her solution concurrently with #1?
I contend that that leaves us with just "Cat" and "dOg" as possibilities, which student #3 would recognize, and choose cat or dog, depending on whether he had an a or d.
The other solution leaves "has" as one of three possibilities coming to #3, and since "a" is not f=1, that leaves only "dog" as the answer.