The white rook is attacked and obviously must move somewhere. Kudos to anyone that found the correct move, 1.Rd2! (or 1.Rd3! works just the same). These two moves are the only ones that win. Everything else draws.
The natural move, 1.Rd1, which was my choice, only draws. The line is as follows.
1. Rd1 d4
2. Kd7 Kd5!
3. Kc7 Kc5!
And the black king will keep the white king at bay with the opposition. If the white king ever tries to outflank the black king, with something like 4.Kb7, then black just replies 4.Kc4 and the white king is too far away.
Note that if black doesn't play accurately after Rd1, he can still lose, as seen here.
1. Rd1 d4
2. Kd7 Kd5
3. Kc7 Kc4??
4. Kd6 Kc3
5. Ke5 d3
6. Ke4 d2
7. Ke3 and white wins the pawn and the game. The key move is 4.Kd6, which allows the white king to access the pawn from the opposite side of the black king.
The reason 1.Rd2 wins, is that it allows white to lose a crucial tempo.
1. Rd2 d4
2. Kd7 Kd5
3. Rd1! and now the black king must choose either c5 or e5, both of which would allow the white king to invade on e6 or c6, respectively.
This is an amazing puzzle to me because when looking at the initial position, the thought "I'm white, I need to lose a tempo here" is so subtle. Positions like this feel like a race, that we need to get our king to help with the pawn as quickly as possible. But to think this problem is actually a lesson in the opposition is just really cool. I love positions like this one, that seem simple but have a very deep point.
