Originally posted by David113
Construct a game which ends in the above position.
12 Black units + 4 wP captures = 16
...Rg2xg1+ can't be the last move, because then there is no way to unlock the SE corner. Last move must have been h2xg1=R+, so
9 White units + 7 wP captures [h2 came from c7!] = 16
All units were either captured by pawns, or are present in the diagram. Color-sensitive captures: wB must have died on g6 - no other light square available.
Before my laptop crash, I was trying to decide if White promoted the missing h-pawn or not. I have concluded that both possibilities work, and the problem is cooked.
The h2 pawn did not promote, but rather was captured on h2.
The advantage is that I can uncap h7xg6 immediately. The only worry is getting the wRh1 home, so...
Retract 1...h2xRg1=R+ 2.c2xRd3 h7xBg6. Both sides have free pieces to move now, so I will just show the general plan of retraction rather than plod through move by move.
-bNg4 goes home. bQ exits via h3 to a1, and unpromotes.
-bPa steps back far enough to allow a2xBb3.
-Black gets Bb3 out of the way and unpromotes Bb1.
-bPb steps back far enough to clear the way for White pieces.
-bK to f1, wR to g2, bBe1 to g1, bK to e1 lets wR exit via f-file. wK exits via h3 and heads to Qside.
-bK exits via h3 and returns home.
-wR returns home to h1.
-wBg6 returns home to f1.
-g3 pawn steps back and lets Bg1 return home.
-Rd3 returns to h8.
The position is obviously legal at this point [has been for quite some time].
White promoted his h2 pawn.
Retract 1...h2xNg1=R+ 2.Nf3 Qh3. Again, both sides have free pieces to move, so let's think in plans and not move-by-move.
Black obviously has to wait on the g6 uncap until the pawn unpromotes, so...
-Ng4 and Qh3 return home. Nf3 runs around.
-bK to f1, bBe1 to g1, bK to e1 allows the escape of the Kings as in sol. 1.
-f2xBe3! uses Black's promotional possibilities to help White. Be3 goes home. g6 steps back.
-wN goes to h8 via g6, then unpromotes.
-wPh steps back to h5.
-c2xRd3 puts a Rook on the board, which returns home to h8.
-g5 steps back, then h7xBg6 puts wB on board.
-wBg6 returns home. g3 steps back.
-wPh2 uncaptures every missing White piece [Q, 2R, 2N], returning home to c7.
-all the White pieces just uncapped scatter to allow bBg1 to travel to a1 and unpromote.
-bPa steps back, a2xBb3, Bb3 clears, unpromote b1, bPb steps back etc, just like sol 1.
Again, an obviously legal position.