A won position is not enough if the final mate takes too long or ends in stalemate. These four mates against a bare king are the ones to know by heart: king and queen, king and rook, two rooks, and the rare bishop and knight.
Verdict White wins.
Drive the king to the edge with the queen, bring the king up and mate on the edge, without giving stalemate.
The red squares show where the black king cannot go. The queen keeps a knight's move away from the king, so it cuts the king off and cannot be taken, and the squares left to the king shrink with every move.
1. ♕e7 ♚c6 2. ♔d2 ♚b6 3. ♔c3 ♚c6 4. ♔c4 ♚b6 5. ♕d7 ♚a6 6. ♔c5 ♚a5 7. ♕b5#
Stalemate. In the exercise position, 1. ♔d3?? leaves Black without a legal move, and the game is drawn.
White to move. Mate in one.
White mates with ♕d2#. Careful: 1. ♔d3??, 1. ♔b3?? and 1. ♔b2?? are all stalemate.
1. ♕d2#
The king on c3 protects the queen on d2, and the black king has no escape square.
Copy the position into any board or engine to practice it:
8/8/8/3k4/8/Q7/8/2K5 w - - 0 1
Verdict White wins.
Use the king to shrink the box and the rook to mate on the edge, with the kings facing each other.
The rook cuts the king off along a file, and the king walks up beside it. Every time the rook takes away a file or rank, the king moves up to hold it. The red squares show the squares the black king is denied.
1. ♖d2 ♚b5 2. ♖c2 ♚a5 3. ♔c4 ♚b6 4. ♔b4 ♚a6 5. ♔c5 ♚b7 6. ♔b5 ♚a7 7. ♔c6 ♚a8 8. ♔c7 ♚a7 9. ♖a2#
Leaving the rook next to the king without protection. In the exercise position, 1. ♖a3+?? 1... ♚xa3 and the rook is lost.
White to move. Mate in two.
White mates in two, and the first move is a king move.
1. ♔c5 ♚a5 2. ♖a3#
♔c5 takes away the squares next to the black king, and after ... ♚a5 the rook mates with ♖a3#.
Copy the position into any board or engine to practice it:
8/8/8/2k5/8/1K6/4R3/8 w - - 0 1
Verdict White wins.
Push the king to the edge with the ladder: one rook checks along a rank while the other cuts off the next rank.
The rooks climb the board like a ladder, one rank at a time. The king cannot cross the rank held by one rook, and the other rook gives the next check. The two rooks stay far from the king, so it cannot attack them.
1. ♖c5+ ♚e6 2. ♖h6+ ♚d7 3. ♖a6 ♚e7 4. ♖c7+ ♚d8 5. ♖h7 ♚e8 6. ♖a8#
Putting a rook next to the king. In the exercise position, 1. ♖g8+?? 1... ♚xg8 loses a rook.
White to move. Mate in two.
White mates with the ladder: ♖c7 first, then a mate on the back rank.
1. ♖c7 ♚e8 2. ♖g8#
♖c7 cuts off the seventh rank, the king can only go to e8, and ♖g8# mates.
Copy the position into any board or engine to practice it:
8/2R5/8/5k2/7R/8/8/5K2 w - - 0 1
Verdict White wins, but only in a corner of the bishop's color.
Drive the king to a corner of the bishop's color, then mate with the bishop, the knight and the king together.
The bishop is dark-squared, so the mate can only happen in the corners a1 and h8. The black king is already on a1. The bishop holds the long diagonal, and the knight and the king close the other squares.
1. ♔b3 ♚b1 2. ♗f4 ♚a1 3. ♘d6 ♚b1 4. ♘c4 ♚a1 5. ♗e3 ♚b1 6. ♘a3+ ♚a1 7. ♗d4#
Driving the king to the wrong corner. A king in a corner of the other color cannot be mated, so the king has to be pushed along the edge to the right corner.
White to move. Mate in four.
White mates in four. The bishop is light-squared, so the mating corner is h1.
1. ♘e6 ♚h1 2. ♘f4 ♚g1 3. ♘h3+ ♚h1 4. ♗e4#
The knight tightens the net, and the bishop gives the final mate on the long light diagonal.
Copy the position into any board or engine to practice it:
1B6/1N6/8/8/K7/8/8/k7 w - - 0 1