one move mate
Stanley Collings

The one move mate was described in MANIFOLD - 12. Unfortunately the problem was incorrectly stated: the clue should have read that White's QRP moved TWICE (not once) in the last ten moves. F'or those who still cannot see the solution here it is.

Holmes got straight down to the solution.

Only one black pawn is missing, and this became the bishop (on e5). I shall show that on its promotion route this pawn checked the white king thereby causing it to move; thus 'white castles' is no longer a legal move. More strictly I shall suppose that the pawn avoided giving check, and then demonstrate that the board position is impossible on this hypothesis.

The natural and obvious candidate for promotion is black's QP. To avoid giving check, this must have promoted on c1 (having captured from b2) or on a1. In either case three pawn captures are required. In.addition the bishop originally on fl must have been captured by a knight, and this accounts for all four captures by black.

The obvious candidate for the white promotion is the QktP, and this must have captured three times to by-pass the black pawns and reach a white promotion square. Thus the tally of white captures is:

       by QKTP    3 
       by P(e6)   1 creating the doubled pawns 
       by P(f5)   2 creating the pawn inversion 
       by Kt(say) 1 capturing B(f8)

       TOTAL      7

But this is impossible as white made only six captures in all.

'That completes it,' exclaimed Watson. 'Black's Qp must have checked the White king, and castling is illegal. The solution must therefore be P x P e.p. A wonderful exhibition of your analytical skills.' Holmes was displeased rather than flattered. 'When have you known me satisfied with the superficially obvious? Besides, if you had more of the analytical prowess you keep extolling in me, you would not have overlooked an essential part of the data. White's RP moved twice in the course of the last ten moves.' Holmes continued with his exposition.

It is natural to suppose that Black's QP promoted, but it is not certain that it did so. It could, prima facie, have captured its way to b5, leaving the QKTP to promote on a1. If the KtP captured away from the b file before the QP captured on to it, White's QKTP would have had a clear run to b7, and the earlier deductions would not hold. The captured white pieces consist of the bishop on f1 (taken by a knight), a black square bishop which could not have been taken by the supposed QP at b5, and two knights. Therefore the QP took both knights and the QKtP took White's 'black' bishop; but where? It must have been after white's QRP reached a4 but before White's QKtP reached b4. Furthermore, P(b5) must have captured from c6 after white's QKtP got past.

Counting 10 white moves back from the board position gives:

       1. P(a5) - a4 
       2. B(d5) - a8=P 
       3. P(a8) - b7    uncapturing a rook. Black P(b5)
                        uncapturing Kt.
       4. P(b7) - b6    Meanwhile B(e5)unpromotes on a1
                        to a pawn which retracts to a3.
                        The black king has to move aside to
                        allow this to happen.         
       5. Kt(b5) clears out of way 
       6. Q(b4)  clears out of way 
       7. P(b6) - b5 
       8. P(b5) - b4 
       9. P0b4) - b3 
       Black P(a3) - b4 uncapturing bishop 
      10. B(a3)  clears out of way 
      11. P(a4) - a3 

Thus QRP can have moved twice in the last 11 moves, but not in the last 10. Hence it was Black's QP which promoted and so the White king has moved.

Holmes sat back in his chairs but was still brooding. 'The position is still interesting. If we make the simplest of changes, moving P(c7) to d7, White again has a mate in 1; but now the outcome is different. I wonder whether that fellow Collings in aware of this final twist?'