Bishop and knight checkmate

King, bishop, and knight can checkmate a lone king, but their coordination is difficult. The bishop controls only one color of square, the knight covers squares by jumping, and the attacking king must close the gaps. None of the three pieces can fully replace another's function.

The correct corner

The final mate can be forced only in a corner whose square color matches the bishop. A light-squared bishop needs a light corner, and a dark-squared bishop needs a dark corner. The defender tries to reach the opposite-colored corner because the final checkmate arrangement cannot be completed there.

A practical plan

1. Use all three pieces to reduce the available space and drive the enemy king toward an edge.
2. Prevent it from settling in the wrong-colored corner and guide it along the edge toward the correct one.
3. In the final net, the bishop checks or covers the diagonal, the knight removes one exit, and the attacking king covers the others.

This ending is more demanding than two-bishop checkmate because bishop and knight control the board in very different ways. One inaccurate move can let the king return toward the center and force the attacker to repeat much of the work.