Chess

I came across this position in the book Endgame Magic (Batsford, pounds 9.99), a compilation of endgame studies, all described very clearly by John Beasley and Timothy Whitworth. This one, composed by A Mandler in 1924, features a duel between bishop and knight. It is White to play and draw.

Without his pawns, White would draw easily, but as things stand, he is hard pressed to prevent the knight delivering mate on c5 or b2. In fact, if the knight ever reaches any of b7, d7, e6, c4, e4, b3 or d3, White is dead.

But things are even worse than that, for we can now see that the knight must never be allowed to reach e5 (threatening to move to d7, c4 or d3) or f2 (eyeing d1, d3 and e4) because the bishop cannot guard against all the threats simultaneously. All of which means that the knight must be kept out of f7, g6, g4, f3, h3 and h1. And we can now add g5 and h7 to the forbidden zone, since the knight on g5 would threaten to move to f7, e6, e4, f3 or h3.

Continuing in this manner, you may deduce that if the knight is on: a8, c8, d8, e8, f8, g8, a7, c7, e7, g7, d6, f6, h6, d5, f5, h5, d4, f4, h4, e3, g3, c2, d2, e2, g2, h2, a1, b1, c1, e1, f1, or g1, the bishop must move to e4, f3, d5, e4, f5, g6, g4, f5, h5, d5, d5, f5, h5, g4, f3, e4, d5, f5, h5, e2, d5, f3, d5, e6, g4, e2, d1, e4, c4, e2, f3 and g4 respectively! In the diagram, 1.Bh5! is the only move to draw. An amazing concoction of related squares.