This article looks at basic checkmates -- the kind every chess player has to recognize on the board in order to finish off a win. These basic checkmates will all be presented as mate-in-one problems; if you like, you can try to find the checkmate in each diagram first, and then read the explanation and answer below to see if you were right.
Our first example uses a queen and rook together to deliver a checkmate. However, this same pattern can be accomplished with any two major pieces.
A lone king against the edge of the board is easily checkmated by any two major pieces. While one piece prevents the king from moving away from the edge, the other can move to the same rank or file as the king to deliver checkmate.
In the example above, the White rook is patrolling the seventh rank, preventing the Black king from moving off of the eighth rank. Since the rook is already doing a good job of keeping the king hemmed in, it can stay where it is. Instead, making the move Qa8++ finishes the game, as the queen and rook combine to take away every square the king might flee to.