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Don't think it is legal...
The king might have sat on f7 via a6-b7-c8-d8-e8-f7 but after going to f7 the knight has no way to get into e8. d6 is the only way which checks the king forcing it to capture the bishop.
I don't see any other way.
"No, it's not legal" is almost never the correct answer in a retro.
It looks like the white's first capture had to be a rook, and the second could be a rook or a queen.
Still not correct, Frankwho. Your starting position is illegal.
I actually nearly worked it out but haven't had chance to test it. Unfortunatly someone beat me to it (i did figure the above out indepentantly) if you substitute the Lower rook with a queen (i.e. not the one on the 8th rank) it might work, but i'm not sure?
Summersoltice is correct. The last move must have been white Bg8xQh7. Full logic as follows, to illustrate the thoughts that go into these problems.
White's king is behind black's pawn chain, so it must have entered from a6-b7-etc. But black's knight needs to come to e8 after wK has crossed e8. At that point the wK cannot be on f7 as bN needs to come in Nd6-e8, and d6 would be check. Therefore wK must have been on g8/h7/h8 when the bN came in, and only after that the bK walked in via h7-h8.
From the diagram position, what was the last move? It can't have been bN from d6 (illegal check), and it can't be b6-b7 (the wK needs to have come in via b7.) Therefore the last move must be white's bishop from g8 to h7, possibly a capture.
If Bg8-h7 was not a capture, again black has no last move (bKh7-h8 is impossible, as the king would be in check on h7 and white would have had no way to deliver this check.) Therefore Bg8-h7 must have captured a black piece. Not a knight (bN must have come from h6, which is illegal check) and not a bishop (no last move again). So either a rook or a queen.
Now we ask: how did a wB get into g8/h7? It can't be from g6 (black clearly played h7xg6 so that line is closed), nor can it be from f7 (wK needs to play Ke8-f7-g8-f7 as we established earlier, and it happened before the bK got to h8, which was before wB got to g8, so that line is blocked.) Therefore the wB is promoted via h7xg8=B after white's king went f7-g8-f7. What was captured on g8? Not a bQ or B (check), not an N (again illegal check) so it must have been a rook; h7xRg8=B.
So one of black's rooks was captured on g8. The other couldn't escape from the corridor along a8-e8 because of the black pawns and the immobile bishop on f8. Black has all 8 pawns, so didn't promote to a rook. Therefore the piece the wB captured on h7 was not a rook either, so it must be a queen. Therefore the last move must have been wBg8xQh7. Before that black's move was Qh7 from somewhere, and the position is "clearly" legal. Summersolstice gave a sample proof game.
Composers generally don't give illegal positions. Retro composers in particular make positions where the point is that the position is legal but must have involved very specific moves/sequences no matter how you try to reach the position. The following one might be on the very tricky side of "easy" - can you find a game leading to it?
Veisberg, Y. & Ya'akov, A.Fairy Chess Review 1948
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