Back in the twenties French endgame composer Henri Rinck published a series
of compositions in which each side had exactly two rooks--no pawns, queens or minor pieces--Only king and two rooks.
Let's have a look at some of Rinck's Rooks:
H. Rinck, La Strategie, 1921
White is to move and win. Since all endgame studies take advantage
of the special placement of the pieces the first move has to be a forcing
move otherwise Black will reposition his forces more favorably.
1. Rd6+ Ke7 (Kc7
leads to the same thing)
2. Rh7+ Ke8
Here Black could have interposed with the rook on f7. This rook is
easily lost to a skewer but there is a subtlety. Let's take a detour from the main line and check out a trap hidden in the position:
Variation after 2. . . . Rf7
3. Rd7+ Ke8 (setting
a trap)
4. Rhxf7??
Falling into the trap! The correct move, which simply wins a rook, is to take with with the other rook. (This
trap has the virtue of preying on right handed players since the h7 rook
is more in the "trajectory" of the right hand.)
4. . . .
Rg6+!
Variation after 4. . . . Rg6+
And Black has a draw because of the "stalemated" position of the Black King.
White will not be able to escape the checks by capturing the rook with his
king without stalemating Black. Also blocking the check by one rook
ends up losing the other rook.
5. Kd5
Rg5+
6. Ke6
Rg6+
Variation after 6. . . . Rg6+
Again White can't interpose the rook (lifting the stalemate position) without
losing booth rooks.
7. Kf5
Rg5+
8. Ke4
Re5+
9. Kd4
Re4+
10. Kc5 Rc4+
Variation after 10. . . . Rc4+
White cannot escape the checks.
Back to the main line. Here's the position again after 2. . . . Ke8
(instead of 2. . . . Rf7)
3. Re6+ Kd8
4. Ra7
Position after 4. Ra7
Black cannot avoid mate next move
OK now it's your turn. Here's another study by Rinck with a solution similar to the previous one.
Try to solve it