Mr. P and Mr. Q know that there are 16 playing cards in the desk drawer: hearts A, Q, spades 4 J, 8, 4, 2.

1, from the sentence of 1, this number is repeated, which can be a, 4, 5, q.

2. It can be inferred from the second sentence that Q knows that what P sees is not a number that only appears once, and the numbers of hearts and squares are repeated, so he sees hearts or squares.

3. In the third sentence, P infers from Q's words that Q sees a red heart or a square, and knows the correct result according to the number he knows, which means that the number he sees is not A, otherwise he doesn't know. It can only be Q of hearts, 4 or 5 of diamonds.

4. In the fourth sentence, Q infers that what P sees is not A after knowing that P can deduce the correct value. If Q sees a heart, he can't infer the correct result, because there are two possibilities: Q and 4. But Q said that he knew the result, which means that he saw a square. After excluding A, he could determine the result.

So this card is five diamonds.