they might be legal but i know
#5724
Both are illegal. The white bishops c1 and f1 must be captured by knights. The last move must have been Rxf8+. For 8 rooks 6 need to be promoted and that needs 3 pawns capturing towards the a- and h-files. Only available for capture: Ra1, Nb1, Qd1, Ng1, Rh1, h2. So only 6 captures available and 7 required = illegal.
#5724
The black pawns need six captures to reach the open files to promote to the extra rooks. In the first position, not counting the white bishops that are captured at home, White only has five men available for capture, so Black is one short of enough captures and the position is illegal.
In the second position, the white queen gives Black the extra needed capture and the position is legal. Here's a proof game.
There is definitely some math to some of the positions, and probably even more for the positions in the Shortest Proof Game thread.
This is a common trick puzzle, because it appears in a semi-famous book, but is it possible for this position to be reached with white to move?
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Regarding your position, White used all seven available captures getting the queen-side pawns into place. Black made two captures by pawns, with at most one more capture available.
The position is illegal because Black has an abducted h-pawn. What is that? It's a pawn that could not have been captured, could not have promoted, and is no longer on the board.
Would the position be legal if the white g-pawn were removed?
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Your opinion though. Sometimes you must lie in order to live.