No. 120 , Jan. 1997 - SOLUTIONS

3682 - Leonid Borodatov

White captures are cxb, dxc, exd, gxfxe, hxgxf, and the a-pawn on its own line. The capture on the b-line was necessarily the missing black b-pawn, since that pawn couldn't have promoted without a capture. Black has no possible last move. To give black a retro-move, white's last move must've been b2-b4, and play before that was Qe3-a3 Rb3-a3.
So mate in 1 with 1. .. cb3#!, and not 1. Ra3? or 1. Qb2?.

3683c - Stanislav Vokal

Suppose white can castle. The bishop on h3 is the promoted a-pawn, and this pawn needs 5 captures to promote, and keep white's castling intact. Together with the capture on the g-line these are all the captures black did. White's pawns captured 4 times, and together with the missing bishop from c8, these are all the captures white did. So the h-pawn had to promote on h8 to get to a square it could get captured. So black can't castle.
1. OOO! ~ 2. Ra3 3. Ra8#

3684 - Alexander Zolotarev

Last moves were: -1. .. f6xBe6 -2. Bc8-e6 f4xNg3 -3. c7-c8=B e5xNf4 -4. b6xRc7. Further retracting involves unpromoting the two uncaptured knights on c8, uncapturing c7xRd6 and d6xRe5, uncapturing a black-squared black bishop by one of the white pawns on the queen wing, unpromoting the two uncaptured rooks on g8, bringing back the uncaptured bishop to f8, and uncapturing a white rook on f6.
The position can be unlocked with only one queen move: Qh1-h2.

3685 - Jean-Michel Trillon

3686 - Thierry Le Gleuher

3687 - Thierry Le Gleuher