Chess

White to play and mate in five.

This problem by A. Popandopoulo won first prize in a Soviet chess magazine problem composing tournament in 1940.

White's problem here is how to dig the black king out of its bunker. With both black knights pinned, there is clearly a danger of stalemate, so White must find something to do before moves of the black f-pawn run out. The proto-solution must therefore begin something like this: White plays a move; Black plays fxe6 or fxg6; White unpins one of the black knights; White plays another move; the knight hops right back where it came from ... and then what?

Somewhere along the line, White must get rid of one of those knights without delivering stalemate. Of course, if he could capture the knight with check, it might even be mate, and that's the clue to the answer.

The knight on g1 can only move to e2 or f3, both of which could be controlled by a bishop on the d1-h5 diagonal; the knight on g2 can only move to e1, e3, f4 and h4, all of which can be covered by a rook on e4. Now all we have to do is put all the pieces together. The basic line works like this: 1.Ra1! fxe6 2.Bb1! Ne2 3.Bc2+ Ng1 4.Bd1 Ne2 (or Nf3) 5.Bxe2 (Bxf3) mate; or 1...fxg6 2.Rd5! Nf4 (or anywhere else) 3.Rd4+ Ng2 4.Re4! any 5.RxN mate. Just two more lines tidy up loose ends: 1...f6+ 2.Kf5 fxe5 3.Rxc4 e4 4.Rxe4 and 5.RxN mate; and 1...f5 2.Bh5 f4 3.Bd1! f3 4.Qxf3! Nxf3 5.Bxf3 mate.