Shuttling back and forth between g7 and h7 won't work, because the White king will make its way to b1, force the rook off the second rank, and then start moving toward the a-pawn. So, Black has to try something else. ...Kf6-e5-d4-c3-b3 comes to mind, but it will fail to a rook check, when White queens. However, ...Kf7-e7-d7-c7-b6/b7 looks good, because a rook check on the eighth rank will result in black's taking the white rook and still stopping the pawn with his rook, while otherwise, Black will win the a-pawn. (Note that it's not important that it be Black's move.)
Useful Ending Idea
Sort:
Why moving the king to f7-e7-d7-c7-b7 doesn't work (highlight to see) (Don't look at the board if you still want to solve it):
Once the black king gets to e7, White will push his pawn to a7 (provided he left his rook on a8). Because after the Black king gets to e7, the White rook will go to a8 regardless of what Black does. The Black rook can't take the White pawn or else it'll get skewered, while it is too late for the Black king to return and the Black king is still too far to prevent the pawn from queening.
Sep 1, 2011
0
#4
You're right--once the pawn is on a7, the king has to stay on g7/h7, as I remembered but forgot. But how does Black live after White's Kf1-e1-d1-c1-b1, chasing the rook up the board and then following with the king to support the pawn?
Oh! I think I see! You *let* the king move up the board, but you come back to a1 and then check forever on a1/b1. If the king comes back to b7, the rook just moves up the board to, say, a5. White never queens.
This is one of my favorite endings. Though exact moves aren't important, concept is: try drawing.