No.1663 (AB)

a) {Draw (dead position) First suppose, as is conventional with a study, that it's White to move. What could Black's prior move have been? R: 1. Ka4-b4? Impossible double check R: 1. Ka5-b4? Previous White move was Ra1xa3[~]+,Ra2xa3[~]+, but no Black unit on a home square. R: 1. Kb5-b4? Previous White move was dxc4[~]+, but no Black unit on a home square. Black's only capture possible is of Q, because anything else would have resulted in a White unit on a home square. If bK just captured wQ, it doesn't make anything easier. R: 1. Q~-c3? Previous White move was Q~xd2[~]+, but no Black unit on a home square. R: 1. Q~xQc3[-]? Previous White move was Q~xc3[~]+, but no Black unit on a home square. Therefore it's Black to move, and the following moves are inexorable: } 0... Qc3*d2+ 1.Be1*d2[+bQd8]+ Qd8*d2[+wBc1]+ {... with an infinite perpetual check. But because we used retro logic to determine Black had the move, the dead position rule is triggered, and the game ends right now in dead position. A perpetual check is still fun, whether it's played out or (as here) a ghost dance happening only in our minds.} b) wRe5-->f5 {Win for White (unique mate in 2) Now Black's last move might validly have been: R: 1. Qh8-c3 Q~xRd2[-]+ or R: 1. Qh8xQc3[-]+ Q~xRc3[-]+ So it's ok for White to have the move. 1. Qxc3[+Qd8+]#? because it would be self-check. The fastest mate is:} 1.Rf5-d5 Qc3*d2 + 2.Be1*d2[+bQd8] #