Chess
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Your support makes all the difference.This White to play and win study by Mark Liburkin is an old favourite of mine. It has the highly unusual feature that you do not begin to appreciate the difficulties of the problem until you are half-way through the answer.
The start is easy enough. If White does not win some material quickly then the game will be bound to end in a draw. 1.Rh8 Bg1 leads nowhere, but the position of Black's minor pieces in that line should set us on the right path. Try attacking the bishop from the other direction: 1.Ra2! Bg1 (1...Nf1 loses simply to 2.Ke1) and now 2.Rg2 attacks both knight and bishop, winning a piece and leaving White rook for pawn ahead.
That, of course, is not all there is to it, for the first serious problem for the solver is finding how Black now manages to put up a fight at all. The answer is surprising: 2...Kf3! 3.Rxg1 Kf2! The white rook has only one safe square, and at first sight it looks as though 4.Re1 wins without difficulty, but just look at the position after 4...e4 and you will appreciate the real problem. Black threatens 5...e3 followed by 6...e2+ 7.Kd2 Ne4+ (or Nf1+). The White rook cannot move and 5.Kd2 allows an immediate draw with 5...e3+! 6.Rxe3 Nf1+.
So how is White to extricate himself? The only hope is to do something with the knight, but with f5 and h5 covered by the black knight, it is difficult to see where it should be heading. After 5.Ne6 e3 6.Nd4 (or 6.Nf4) Black escapes with a remarkable draw by playing 6...e2+! 7.Nxe2 Nf1! 8.Nf4 (as good as anything) 8...Ne3+ 9.Kd2 Nf1+.
The solution is wonderful: 5.Ne6 was correct, but after 5...e3 White plays 6.Nc5!! The threat of 7.Nd3+ now forces Black to continue with his plan: 6...e2+ 7.Kd2 Nf1+ (note that e4 is covered by the white knight, preventing a check on that square) 8.Kc1! Kxe1 (8...Ke2 9.Kc2 also wins for White) 9.Nd3 mate!
The final position, with knight winning against knight and pawn, is a splendid achievement from such a natural starting-point.
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