Originally posted by Mephisto2
White moves and forces a draw
As other posters have suspected, this one involves both castling and the 50-move rule.
13 White units showing + 3 bP captures = 16 [no spare captures]
Black P captures were axb4 [not axb6?? shutting in Bb8] and h7xg6xf5 [the immediate retraction h7xg6?? shuts in Bg8]. No other captures were made.
White is missing a Q, N and P. The missing P is a2 [no wP caps allowed] and it promoted [a pawn on the a-file could not have sacrificed itself to a bP].
The key is indeed 1.0-0-0, as most solvers would probably guess before doing the grunt work. The main idea is to prove that Rf8 is the original Rh1. If so, we'd have to get him home before retracting f3-f4. First, we must eliminate the possibility that Rh1 was captured somewhere.
possibility 1): axb4
It cannot retracted until White un-promotes on the a-file. To do that, we must somehow get Bg3 to f8, retract g7-g6, retract bK and bQ home, retract Bg8 back to c8, then retract b7-b6, all so we can free the promotion square with Nb6. The problem with this plan is that Bg3 cannot escape until the f4 pawn retracts, which is waiting on the very Rook I hoped to uncapture. Note that Bf1/e2 for White also locks out the Rh1, so the bBg3 cannot escape that way either.
possibility 2): g6xf5
I need to retract Bg3 to f8 and g7-g6 before this uncapture, but we have already established the bB cannot leave in poss. 1) above.
So, Rf8 must be Rh1 by elimination. The problem is that he must somehow get past both Black Rooks. Only by sending all the Rooks to the Queenside (!!) can we buy enough space to accomplish this. The plan goes:
[Counting only Black's moves at first...]
3 Qe5 Bh7-g8 [while wR goes to h6]
6 Kb7-f6 [better to just get him out of the corridor]
1 Bh7 [to let wR go to Qside]
13 Rf3-b2, Bg8-h7
13 Rf2-a2, Bg8-h7
[now with bR's clear, we count White's moves to get the R home, not counting the actual retraction to a3, since it's part of the same full move as Black's final Ra2]
The retraction runs:
1...Bh7 2.Rg8 Qe5 3.Rg7 Bg8 4.Rh7 Kc8 5.Rh6 Kd8 6.Ba7 Ke8 7.Bb3 Kf8 8.Be6 Kg7 9.Bd5 Kf6 10.Rh7 Bh2 11.Rg7 Bh7 12.Rg8 Rg3 13.Rb8 Rg5 14.Rb7 Rh5 15.Bb8 Bg8 16.Rba7 Rh7 17.R7a3 Rg7 18.Rd3 Bh7 19.Be6 Rg8 20.Ba7 Rb8 21.Bd5 Rb7 22.Bb8 Ra7 23.Be6 Ra2 24.Bd5 Rb2 25.Be6 Rf3 26.Rc3 Rg3 27.Rd3 Rg5 28.Rc3 Rh5 29.Rd3 Bg8 30.Rc3 Rh7 31.Rd3 Rg7 32.Rc3 Bh7 33.Rd3 Rg8 34.Ba7 Rb8 35.Rc3 Rb7 36.Bb8 Ra7 37.Rd3 Raa2 38.Ra3 Rb3 39.Ra7 Rc3 40.Rb7 Rb3 41.Ba7 Rc3 42.Rb8 Rb3 43.Rg8 Rc3 44.Rg7 Bg8 45.Rh7 Rb3 46.Rh5 Rc3 47.Rg5 Rb3 48.Rg3 Rc3 49.Rf3 Rb3 50.Rf1 Rc3 51.f4f3
1.0-0-0 is the 100th ply with no pawn move or capture, so White gains a draw by the 50-move rule.