Rook Exercise
It's White's turn. Assuming optimal play, what is the minimum number of moves to win the game?
Combinatorics Bonus: Can you count all possibilities (including helpmates and non-optimal) with the minimum number of moves?
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1 solution
First White Rook moves anywhere. If Black King moves left 1 square, then rook 1 file to the left, and after black king moves, white rook goes to the 8th rank to checkmate. Similarly, if the black king moves right, then the rook one file to the right of the black king, and after the king moves again, we mate him on the 8th rank. Total moves = 3 .
Total # of possibilities(w/ optimal play): 9 moves not along d or f-file, 2 moves for king, forced moves for rest. 2 moves onto d-or f-files, forced moves from there. Total: 18+2= 20 possibilities
Total # of possibilities w/ any play: 9 moves not along d , e, or f-file, 2 moves for king, 10 moves for rook, forced moves. So 180 for this case. 2 moves on d- or f- file, 1 move for king, 5 moves for rook, forced moves. So 10 for this case.
Finally, 4 moves on e-file, 2 moves for king, 5 moves for rook, forced moves. so 40 for this case.
180+ 40 + 10 = 230 total possibilities .