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Counterfactuals in chess problems

The problem below is quoted from John Rice’s article “Just for a change” in The British Chess Problem Society’s magazine The Problemist Supplement #90 (September 2007).

Comins Mansfield
4 Pr Chess Amateur 1919

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#2 (Mate in 2)

This problem is a nice, simple illustration of the importance of the counterfactual in chess problems. In many chess problems, as well as the ‘key’ (i.e., the right answer), the full solution - and a full appreciation of the problem - incorporates ’set play’ (i.e., what would happen if it were black to move first) and ‘try play’ (white moves which could be a key but for a single refuting black move).

The problem above has an obvious key - at least it leapt out at me and I am not a strong solver - but the key alone is not really the point. The point is the set play: if it were black to move, then every black move would allow white to mate in one.

However, it’s not black to move, and every white move (but one - the key) spoils at least some of the set play and lets black escape mate. The key messes up some of the set play too, but introduces new mates to make up.

This kind of problem - mates provided for all set play, but no white move which can preserve all of them - is called a ‘Mutate‘.

The problem’s solution is given as a comment.

Entry posted: Tuesday, November 20th, 2007, 10:37 pm ; filed under Chess.
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One Response to “Counterfactuals in chess problems”

  1. Ivan Says:
    November 20th, 2007 at 10:53 pm

    Solution:

    1 ... Sd~ 2 Bxb6
  ... Rd6 2 Qxd6
  ... Rd4 2 cxd4
  ... Se~ 2 Rc4
1 Rf5! Rd4 2 Qxc6
   ... Sf7,g6 2 Qe3
   ... Sf3,g4 2 Qd6
   ... Sc4 2 Sxd3

    n.b.: ‘S’ is for Springer = Knight

    The key sets up a half-battery, so when one of the {BR,BS} moves, the other is pinned.