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Favourite Chess Tactics/Games/Random Positions
Accidents happen – with varying effects.

Often, ‘chess puzzle’ is synonymous with ‘composed chess problem’. Paradox, Tries (near solutions), and Cooks (unintended solutions) are characteristic of chess problems. So, the first requirement of problem solving – cryptic or composed - is to understand exactly what it is the composer is asking.

The two ‘solutions’ submitted seem incompatible but are in fact complementary. One was declared correct, the attached commentary indicating the puzzle was intended to be cryptic – not composed. I decided to keep my head down. However, …

The narrow choice between e3 and e4 risks ambiguity. As locations, they are in themselves not obviously significant; it is their colour complex that matters. Whichever White Bishop is to be added may occupy any legally accessible square of its colour. Thus, there is an array of solutions to choose from – not a unique one. I suggested e6 might be an improvement over e4 to underline this. The former is more plausible because it promises Virtual Play (a variation that follows a Try). I hinted heavily when I said the rubric permitted the use of Retro-analysis and gave a sample variation. I held back one detail but had the rug pulled from under me when the intended solution was announced without notice.

Endorsing one solution does not preclude another. T.R. Dawson (1889-1951) promoted Fairy (unorthodox) chess. He exploited Retro-analysis to prove both the legality and illegality of positions. Examples of his thinking may be accessed via the BCPS link on the CS Home Page: I suggest ‘irreal regions’ is notable.

Placing a light squared Bishop on e4 (or e6) is a Try that fails because of illegality – hence the second solution. By elimination, the White Bishop must occupy e3 – a black square.

This Illegality needs to be proved independently of the intended solution to avoid circularity. Since the Black King is restricted to white squares, he must account for the disappearance of the last light squared White piece from the board. (The same process of reasoning used to produce the intended solution.) Since it is illegal to replace a captured piece on a chessboard - except via a Pawn promotion - there cannot be a White Bishop on e4 (or e6).

So, there are two, complementary solutions to the ‘chess puzzle’. This is such a neat and symmetrical outcome that it is difficult to credit that it is coincidental and not by design. Almost any composed problem solver would see e3 and e4 as an axis round which their positive and negative properties spin in counterpoise - an image that may be more aesthetic than cryptic, but not beyond alert practical players?

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