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exotic chess positions (2)

Juan de Mairena linked in the comments to last post to a truly great retro-chess problem ! In the position below white is to play and mate in three!

At first this seems wrong as there is an obvious mate in two : 1. Qe2-f1, Kh1xh2 2. Rg3-h3 The ingenious point being that black claims a draw after 1. Qe2-f1 invoking the 50 moves rule which states

The game is drawn, upon a correct claim by the player having the move, if
(a) he writes on his scoresheet, and declares to the arbiter his intention to make a move which shall result in the last 50 moves having been made by each player without the movement of any pawn and without the capture of any piece, or
(b) the last 50 consecutive moves have been made by each player without the movement of any pawn and without the capture of any piece.

I’d love to have the ‘official’ solution to this problem. Here’s what I’ve come up with, spending the better part of the afternoon… It will not be optimal but hopefully isn’t too far off. The crucial part is a maneuver unlocking the lower left-hand cluster of pieces (in particular the ordering of white and black rook). All captures were done with pawns and the final pawn move was b2-b3. Immediately before it the situation might look something like the situation on the left (essential is that the white king should not be too far from its home-square as he will be needed later to block the white rook)

after b2-b3 the bisshop on c1 travels to f4 and the black rook squeezes in to block the white rook so that also the black king can come in and position himself at e2. Then the two rooks evacuate the first row, allowing the black king to go to h1 and then the white king comes in to block the white rook from checking the black king (situation on the left below).

Finally, the white rook comes in and positions itself at e2, afterwards the white king evacuates the first row via b2 and travels to the right-hand upper corner entering via g7. Meanwhile, the black rook comes to g1, the white rook then travels to a3 and the black rook to a2. Then, the white king goes to b7 allowing the bishop to unlock the rook on a8 going to g7, allowing finally the king to go to d8…

Perhaps there is a much simpler and more elegant solution, so if you know, please comment. Oh, btw. how is the original problem solved. Well white first cancels the 50-move rule by 1. Kd8xd7 to continue for example with 2. Rg3-g4, 3. Qe1

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