Chess: Logical route to problem solving

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The Independent Culture
TO SOLVE a chess problem you can reach the answer either by logical analysis or by plucking it from the air with your eyes closed, then working out why it works. Today's position is a mate-in-two by the Estonian player and composer Toivo Lukats. If you are uninspired, you ought to be able to work it out as follows:

White cannot afford to wait for Black to kill himself. For example 1. Rxh4 or 1. Qxh4, while ready to meet dxe3 with Qb4 mate, or b4 with Nc1 mate, allow no mating reply to 1 . . . h2] So we can conclude that White's opening move must threaten mate. The most natural tries are with the white queen, but 1. Qd6 and 1. Qf8 (threatening Qb4 mate) or 1. Qb8 (threatening Qxb5 mate) are all defeated simply by dxe3, leaving Black's rook covering b4. 1. Qe5 threatens Qxd5 mate, and prepares to meet dxe3 with Qxc3 mate, but after 1 . . . Rxh5, Black hangs on again. If White's queen could attack c3 and either b5 or b4 at the same time, the problem would be solved, but it can't be done.

Having given up on the queen, we may move to the rook. What about 1. Rxd5? The threat is Rxb5, which is still mate after dxe3 or Rxf4. But it's not the answer. After 1. Rxd5 Rh5] Black staves off immediate mate again.

The rook on c2 and knight on a2 are needed to keep the black king in his box, so we have to look for a mate with the knight on e3. That piece can only give mate from a5, so we are forced to look at 1. Nc4, which is the right answer. 1 . . . dxc4 allows 2. Rxb5 mate; 1 . . . bxc4 allows 2. Qb8 mate and, prettiest of all, 1 . . . Kxc4 is met by 2. Rxc3 mate.