Mate in 1, white to move

Mate in 1, white to move

Pretty simple retrograde.

The e.p. mate is permitted only if ...c7-c5+ could be proved as the only possible last move.

The alternative ...c6-c5 (mate!) seems to allow the further retraction, cxb8=B, but that's a trap! This position (with a WP on c7 and a black piece on b8) looks legal because the number of missing units – 4 black and 8 white – is just enough for all the doubled pawns to have occurred. However, these pawn captures took place on the queen-side, and the missing g- and h-pawns of both players couldn't have been captured there without promoting first. And with no spare units for these four pawns to have captured, they couldn't have gone around one another to promote.

Therefore the position arising from the ...c6-c5 retraction is illegal, and the last move was indeed ...c7-c5+ (previous white move Nc6-a7 or Kd5-d4), allowing the e.p. mate.

Source of this composition?

Knight C8

It's a bit disturbing that white has 2 legal last white moves which is connected to the author idea that the retraction try ...c6-c5+ should actively disable both last white move options. The plus and the minus are therefore locked in the same embrace. I think there is a more elegant solution though.