Here is a simple chess problem from HAKMEM. White to play and win.
8/5BP1/1p6/8/1N6/kP6/2K5/8 w - - 0 1
White's king, and pawn in b3 nearly trap black's king in the white half of the a-file. If the knight under attack in b4 were to move, say Nc6, it would complete the trap. Black's king is of limited use then. Let's assume that black plays b5, or Ka2.
1. Nc6 b5
Without further ado, white promotes the pawn in g7 to queen. Black doesn't have any game left, except to move its king in the a-file, or play b4.
1. Nc6 b5 2. g8=Q b4
White then plays Qa8+, resulting in mate.
1. Nc6 b5 2. g8=Q b4 3. Qa8# (PGN file)