The following position occurs in a real game, right after one of the pieces gets knocked off the board. What was the piece?
It was a black knight. First, notice that the black pawns have moved 14 times diagonally and thus they have taken 14 pieces. Therefore the knocked off piece is black. Since it is impossible both kings to be checked at the same time, the missing piece was positioned on a2. It couldn't be a queen or a rook, because the white king would be checked both by it and the pawn on b3, which is impossible. Therefore the missing piece is either the black white-squared bishop or the black knight. However, the pawns on b7 and d7 haven't been moved the entire game and then the black white-squared bishop hasn't either. Thus we conclude that the knocked off piece is a black knight.