Two rooks, an empty board, and mate in four without your king moving a muscle.
2 a 
g That is the ladder, sometimes called the lawnmower, and it is the first mate I show a seven-year-old because it needs no king play, no opposition and no waiting moves. Just alternation.
Rank by rank, one rook at a time
1.Ra5+ takes the fifth rank away, so the black king has to go up: 1…Ke6. Now the second rook climbs behind him with 2.Rh6+, and because the a5 rook still owns the fifth rank he cannot come back down. 2…Kd7 3.Ra7+ pushes him again, 3…Kd8, and 4.Rh8 is mate on the eighth rank, the a7 rook covering every retreat square.
The rhythm never changes: the rook that is not being used checks on the next rank up. Say it out loud while you play it, “the other rook, one rank up”, and you will not lose your place.
Files work exactly the same way if the king starts nearer an edge. Cut on the c-file, check on the b-file, mate on the a-file. Rank or file, pick whichever edge is closer.
The one thing that goes wrong
The enemy king walks over and attacks a rook. That is his only counterplay in the whole ending, and beginners panic and start moving rooks backwards.
2 g 1.Rg5 costs nothing. The fifth rank is still cut, the rook is now five files away from the king, and Black has spent a move walking to a square that helped him not at all. The rule for the whole ending: when a rook is attacked, move it to the far end of its line, never off the line.
Two rooks give mate faster than a queen does, and they need less thought, which is why I would rather a beginner had two rooks than a queen in a scramble. Once this one is automatic, learn king and rook against king, where you only have one rook and your king has to do half of the work, and try a few rook endgame puzzles to see the same rank-cutting idea with pawns still on the board.