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I found this trick question on r/Anarchy chess:White to move, mate in two.

[FEN "2R2RK/6PP/5P/3PN/P/1pQ3p/n1p1qbp/5brk w - - 0 1"]
[StartFlipped "1"]

The trick is that

you're looking from Black's side, so the white pawn on the H file can promote to a Queen or a Rook, with the only option left for Black to throw their Queen in between.

But is this position actually reachable?

The black and white pawns must've passed eachother, which is not impossible but not trivial either.

36

Even though the board is upside down, the position is still easily legal.

[FEN ""]
[startply "86"]
[StartFlipped "1"]

1. a4 h5 2. g4 h4 3. Bg2 Rh5 4. gxh5 h3 5. h6 e5 6. Nf3 Bc5 7. Nxe5 hxg2 8. h4 Ne7 9. h5 g5 10. Rh4 Ng6 11. Rf4 g4 12. Rxf7 Qh4 13. e3 Bxe3 14. Ke2 a5 15. f4 Qf2+ 16. Kd3 Nc6 17. b4 b5 18. bxa5 Rxa5 19. Rf8+ Ke7 20. f5 b4 21. f6+ Ke6 22. hxg6 Rc5 23. g7 Rxc2 24. h7 Rxc1 25. Ra3 Rxb1 26. Qc2 Rg1 27. Rc3 Kf5 28. Rc5 Kf4 29. Rd5 Kg3 30. Ke4 Ba6 31. Rxd7 Bf1 32. Rdd8 Qe2 33. Kf5 Bf2 34. Kg6 Kh2 35. Kf7 Kh1 36. Kg8 b3 37. Qc3 Nb4 38. d4 Na2 39. d5 c5 40. Rc8 c4 41. Qd2 c3 42. Qd3 c2 43. Qc3 g3
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    Now of course there's a difference between "legal" and "plausible". I'm not sure this position would be that likely to come up in normal gameplay, given that both players make some moves that would be likely considered serious blunders if they were actually competing, missing obvious easy captures and such. – Darrel Hoffman Feb 8 at 14:57
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    @DarrelHoffman You are correct. However, the plausibility of a position is irrelevant in chess problems, so long as it is legal. Of course, illegal positions are still used now and then in good fun. – Rewan Demontay Feb 8 at 15:00
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    How'd you come up with the path to the "starting position" of the question? Just trial/error, or is there some clever way to "work backwards" from a position? Nicely done! – BruceWayne Feb 8 at 16:04
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    @BruceWayne There is plenty of trial and error, but having experience doing it helps. It's about seeing what paths each remaining piece must take, and how that intersects with the possible paths of the missing pieces. Thus, working backwards is done along with trial and error. – Rewan Demontay Feb 8 at 17:14
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    @BruceWayne - Note that the provided moves form one path to the problem's position. There are almost certainly many more. The whole idea with "legal positions" is to winnow down possible positions, eg just randomly sticking a set of pieces on the board. – MaxW Feb 9 at 20:26
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A rule of thumb for these kind of positions that capturing an officer will allow a pair of pawns to pass one another and potentially promote. Capturing a pawn will allow three other pawns to become passed. So you can see that there is easily enough missing pieces to have created this position.

If the issue is that pawns have moved sideways, then the arithmetic is different. Or there may be parity concerns sometimes, particularly if the colour of bishop promotions is important. Neither case applies here however.

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