Basic Checkmate Patterns: K+R

This is by no means the shortest path but probably the simplest.  I'm a firm believer in starting with the simplest methods first.

The Rook cannot use the direct attack method displayed in the previous K+Q combo because the Rook does not attack diagonally.  So the only method is the rank [or file] method.

Here's an example where Black plays sub-optimal moves:  he does not try to attack the Rook but comes back to the square where White has opposition and thus accelerates the Rook check that forces the Black King back [or, in the case of the 8th rank, checkmate].

Note that when White moves his Rook further up, he only does so when he has opposition [the Kings are directly opposed with one square separation and it's our move].  This means the enemy King must retreat:

If the Black King was on d5, the Rook check would allow him to escape to c4.

If the Black King was on f5, the Rook check would allow him to escape to g4.

We do not want to allow the enemy King to move diagonally away from the edge of the board.  We only want him to move laterally or towards the edge.

Here's another example where the Black King moves laterally to attack the Rook, which forces the Rook to move to the other side of the White King.  if Black ever moves back in that direction, White has opposition and can play the Rook forward and drive the King back towards the 8th rank.

If Black keeps running away, he will run out of board and have to reverse direction and at that point, White gets opposition and can play the Rook check.

Notice A) how many more moves this took; and B) how it didn't matter as long as White knows the pattern.

As long as the Rook never moves forward, the enemy King can never escape the box.  And when White gets opposition, THEN he moves the Rook forward.

This is definitely not the quickest mate.  However, it's what I learned and I can execute it very rapidly without having to think, which is necessary in a time crunch.

I showed an example of driving the King towards the 8th rank but it works identically on any edge [1st rank, a file, and h file].  You just have to change directions, in the case of the 1st rank, or orientations, in the case of the a or h file.

When you practice, you'll probably make the mistake of moving the Rook forward at the wrong time, allowing the King to escape diagonally.  No problem; just reset and try again. 

Or, you might accidentally leave your Rook hanging.

Once you successfully do this 10 times, you'll be on your way to being able to execute it in only a few seconds.