1. dxc7ep! b4 2. c8=D,T#

R: 1. ... c8-c6?! and earlier c8=sB?!

Supersession of P1380851

Superseded by P1380851

The 2018 FIDE laws state: "3.7.2 on its first move the pawn may move as in 3.7.1 or alternatively it may advance two squares along the same file, provided that both squares are unoccupied."

Hence Black's newborn 8th rank pawn, which has never been moved before, reserves the right to commence a double-step on its first move, and likewise White receives the right to capture it en passant as they do with a 7th rank pawn.

PRA
1. bxc3ep 0-0! (for AP reasons, not 1...Kf2?/Th2? etc) 2. Ta1 Txa1 3. Kc4 Txa4#
1. fxe3ep 0-0! (for AP reasons, not 1...Tf1?/Txh3? etc) b2 Txf3 3. Tc3 Tf4#

For AP as for anything else, the default meta-convention is PRA before RS. Here we use AP to lock down wK & wTh1, so the last move was R: 1. c2-c4 or 1. e2-e4. There is a different h#3 in either case, beginning with ep and then 0-0.

1. hxg6ep+ Lg5 2. Dxg5#
R: 1. g7-g5 Te3-e7+ 2. Kg5-h6+ Lf5-h7+ 3. Kf6-g5 Sd6-e8+

Black has captured 3 white units. dxcxb accounts for 2. With only one left over, we know that bPh3 never captured. So to explain wPh4, White must have played fxgxh or hxgxh. Combined with dxcxb & exdxcxb, that accounts for all of White's captures.
(a) If White played fxgxh, then the original [wPh] was "waylaid" by an officer, without promoting or capturing.
(b) If White played hxgxh, then the original [wPf] did not capture. We know that [bPf] or [bPg] promoted, using at most one capture.
(b.1) If Black did capture fxg or fxe, then [wPf] did promote to make the balance, and Black's last move can't have been fxg, or the f-file would be blocked to wP.
(b.2) If Black didn't capture fxg or fxe, then [wPf] was waylaid to clear the way for [bPf] to promote.
We don't know which of these three possibilities happened, but in every case:
(1) All captures are accounted for (so e.g. Kg5xSh6 was not possible).
(2) Black did not just play f6xg5.
If Black just played g6-g5, retract prior checking moves and discover retropat as g6 is blocked preventing discovered check by wB now on h7. By elimination, last move was g7-g5 and ep key is ok.

1. Kd7 g4 2. Lh1 Lg2 3. Ke6 Lh3 4. Ld5 g5+ 5. f5 gxf6ep#

1. exd3ep g5 2. Lb3 Se6#

HJ: Black captured all six missing white men with dxe, exfxgxh, and fxgxh.
So White captured all five missing black men with axb, bxa, cxb/d, and e2xf3xg4, and promoted twice.
Last move was d2-d4, because all other attempts give illegal checks, so the ep key is legitimized.

1. dxe3ep+ Kxc4 2. Lc3 Sxc2 3. Ta5 axb3#
R: 1. e2-e4 Tf3-d3+ 2. Ke4-d5

See P0003211

Example Proof Game: 1. b3 a5 2. c4 a4 3. Na3 b5 4. d4 c5 5. Bg5 h6 6. f4 hxg5 7. Nf3 gxf4 8. Qd3 bxc4 9. Nc2 axb3 10. Rc1 Bb7 11. Na1 Nf6 12. Rc3 Nh5 13. Qe3 fxe3 14. Nd2 exd2+ 15. Kf2 Nf4 16. Rg1 Nh3+ 17. gxh3 Bh1 18. Rcg3 Ra6 19. Rg6 Rf6+ 20. Ke3 Rh5 21. Bg2 Nc6 22. Be4 Na5 23. Bc2 bxc2 24. R1g4 Rf3+ 25. Ke4 Nb3 26. Rd6 exd6 27. Rf4 Qh4 28. Rg4 Qe1 29. Rf4 Kd8 30. Rg4 Kc7 31. Rf4 Kb6 32. Rg4 Ka5 33. Rf4 Ka4 34. Rg4 Rhf5 35. Rh4 g5 36. Rg4 Bg7 37. Rh4 Be5 38. Rf4 cxd4 39. Rg4 f6 40. Rh4 Qf1 41. Rf4 gxf4 42. Kd5 Rd3+ 43. e4

1. cxb3ep+ Sb4+ 2. Kb1 Sxe2 3. b2 0-0#
R: 1. b2-b4 Tc3-a3+ 2. Sa3-c2

Black captured 8 white men with pawns. Critically sBd & sBe never captured, therefore White pawns captured onto d- & e-files (to explain the pawn inversions there). Therefore wBb4 did not come from c3.

1. d4 Td2 2. Lc3 Lc1 3. d5+ e5+ 4. dxe6ep+ Td4#

1. bxc3ep+ d3 2. 0-0 Tf4 3. Kh8 Txf8#

Not R: 1. c3-c4? La6xb5? because Black's 10 captures are already accounted for: 6 pawn captures on files a-d, e.g.: bax, cxbxa, dxcxbxa + 4 waylaid pawns on files e-h or maybe 2 more pawn captures if bPe & bPf cross-capture.

No solutions except for those beginning with e.p.
297 candidate solutions begin 1.gxf3ep, but only one includes castling. Queenside 2. ... 0-0-0
22 candidate solutions begin 1.fcxd3ep, but only one includes castling. Kingside 2. ... 0-0
In some way, these are trying to be combined so that from AP perspective, White's last move can only have been double hop with wBd or wBf.
We need a clear delineation of the precise PRA-AP algorithm to be followed.

The point: if this problem is "sound", then surely P1382808 is "unsound", because there only one of the two parts needs to prove that White castling rights remain, so there are 4 cooks.

1. ... Kd2 2. e3+ fxe3#
1. bxc3ep b3 2. Kxd3 0-0-0#

Black has no tempo moves to convert the set play to a main play solution. Rc5~,Se5~,e3,Sf1 all disrupt the set play.
The main play castling is needed both for the mate and for the legitimization.

1. Tb3 Lxc4 2. Txb4 Txa2#
1. Kxb4 Tb1+ 2. Ka4 Lb5#
1. cxb3ep 0-0-0! (Td1?) 2. e4 Td4#

0. ... [-bPg5] 1. Lxb3 Ta8#

Clearly an unfinished move joke. By a usual convention for these things, a player might be halfway through a castling, an en passant, or a promotion. 1.75 is nearly 2.0, so Black would be the moving player.

Black is not in the middle of an e.p. or castling, so the only possibility is a promotion. Black has lifted up the pawn, to replace it with an officer on the 8th rank. However, White has apparently made 12 pawn captures, accounting for all missing Black units, so Black is not part way through promoting a pawn.

Therefore it's not Black in the middle of a move. By a joke application of Article 15, we say that it's *White* in the middle of a move instead. So 1.75 - 0.5 = 1.25 and it's h#1.25.

- White can't be part way through a promotion, because all White pawns are on the board.
- If White were in the middle of castling, then the pawn capture balance would be ok, but Black would have no prior move.
- If White were in the middle of en passant h5xg6, then bPg5 can help with capture balance, but still there is one capture short for the balance.
- So White is in the middle of en passant f5xg6. If we complete the joke move by removing bPg5, then the position is legal, with 12 White pawn captures and 13 missing Black units. A sound h#1 awaits.