The logic behind the solution is remarkable: White cannot mate without covering the d6, b6 and b5 squares, and his king alone cannot do that. Since b4 or d4 cannot be played until the final move, it is essential for White to free his f-pawn, which means capturing on f3 with his king. But Kxf3 is impossible until all the pieces protecting it have been eliminated - and the knight on g1 cannot be taken until the rook on g4 is gone. That takes care of the first 119 moves of the solution: 1.Ke1, 2.Kd1, 3.Kc1, 4.Kb1, 5.Ka1, 6.Bb1, 7.Ka2, 8.Ka3, 9.Ka4, 10.Ka5, 11.Ka6, 12.Ka7, 13.Kb8, 14.Kc8, 15.Kd7, 16.Ke8, 17.Kf8, 18.Kg8, 19.Kh7, 20.Kg6, 21.Kh5, 22.Kxg4; the king then retraces its path, returning to a1 at move 38, then 39.Ba2, 40.Kb1 and 45.Kxg1; next in line is the rook on h3, which involves another circuit ending at move 69, followed by turning round again and capturing the bishop on h1 at move 94. With h2 still under Black's control, White must again go the long way round to reach Kxf3 at move 119. After that, the remaining moves are 120.Ke3, 121.f4, 122.f5, 123.fxe6, 124.e7, 125.exd8=Q, 126.Qxc7, 127.Qb8 and finally 128.b4 mate.
The striking thing about such compositions (and this one is, I believe, the longest of its type) is that none of the early captures alter the fact that the white king has one and only one route through the minefield of black pieces. And even after all the carnage is completed, there is still only one nine-move sequence leading to mate at the end.Reuse content