Arresting the Enemy King
Let's have a look at this position - White has a Rook on a1 and a King on e1 while Black has a king on e5. It's M15 but you've to know HOW. So let's learn how to mate with a King and Rook.
1. We've to set a jail for the black King with our Rook across the board.
2. We've to move our King up to the Black King.
3. We've to set up another jail with the Rook keeping the King in a corner.
4. If it's possible to make the jail smaller, we should do it
5. If it's impossible to make the jail smaller, we should play a waiting move with the King
6. When the Black king reaches the side, deliver checkmate with the Rook.
Here's an example -
1. Ra4
Just like the King and Queen, the Rook makes a jail for the Black King. He only has 32 squares to move to. Black might want to stay close to the centre so he just keeps moving back and forth and that's when we bring our King.
1. Kd5
2. Ke2
Bringing the King up to the board.
2. Ke5
3. Ke3
Getting the king closer.
3. Kd5
4. Re4
The Rook cuts off half the squares for the King and we need to keep him in jail.
4. Kc5
5. Rd4
4 more squares had been cut off.
5. Kc6
6. Ke4
It's impossible to make the jail smaller so moving the King up.
6. Kc5
7. Ke5
The Kings face each other forcing Black back.
7. Kc6
8. Rd5
Rd5 is better than Rd6+ as the latter allows Kc5. Now Black is restricted to only 9 squares.
8. Kc7
9. Rd6
It's now the final 6 squares for the King.
9. Kb7
10. Kd5
The King comes in again
10. Kc7
11. Kc5
Now Black is forced to the corner.
11. Kb7
12. Rc6 (or Rd7+ but let's go with the former. Now Black has only 4 squares) Ka7
13. Rb6
Now Black has only 2 squares.
13. Ka8
14. Kc6
The King moves in for the final blow
14. Ka7
15. Kc7
Forcing Black to the corner.
15. Ka8
16. Rc6#
In move 16 DO NOT PLAY RB7 AS IT'S STALEMATE AND IT'S A DRAW. But this is how you checkmate with a King and Rook