i've got a puzzle from a book and it is mate in 2 for white, it's really hard, i spent 10 minutes but didn't solve it, here it is.
white to move and win in 2
hint: you better look back instead look forward

here is the answer:

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Your premise that Black's Rook and King have already moved could not be right as any chess program gives Black's reply to Qh2 as 0-0-0. Black's pawn or a piece in a previous move could have been captured by White's King or Queen.

interesting.... never thought of that... maybe i am wrong about this puzzle

Well snrao,

white's queen or king might have captured something, but as white moves in the given position it was black to move last. The only possible moves take away the right to castle.
The problem is a completely correct retro puzzle.

YES. I am wrong. The problem is a beauty.

Ingenious!

This one is also a nice retro puzzle, but a bit more difficult.

TR Dawson, Falkirk Herald, 1914
[FEN "3k4/p2P2p1/1N1P1N2/1PpKpP2/2PpP3/3P4/3P4/8 w - - 0 1"]

Mate in 2

Being a 2 mover, White's only way could be 'en passant' and mate next move.. besides, Black's only last move should be pawn double step... but which pawn & which e.p.?... hmm... I am working on it...

So, you only have to proof which one had to move. It's not that difficult.

A little hint below, of course not the solution

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Black's Queen Bishop at f8 has two ways to come out... e7 and g7. Since g7 pawn is at starting position, e7 pawn must have moved for the bishop to come out and die. Had it moved only one step earlier and made another step now, White could not capture it by e.p. Hence it was the other pawn which made two moves, i.e., c7 to c5. So, the key must be, 1. b5xc6 & mate next move. My conclusion must be right but logic could be wrong.
But how on earth this position could be reached? Can we construct the game with legal moves from either side?
Can we construct retro positions and check its legitimacy with any software?
No chess software either commercial or non-commercial could solve such retro problems. Does it mean humans are still superior to computers?

I believe there is problem-solving software that deals with retro puzzles: Natch.

Well snrao,
you are right. The proof is really simple: If you look at white's pawns and count the number of black pieces they must have taken to reach the actual position the number is ten. Counting the black pieces on the board is six. Therefore all missing black pieces have been taken by white's pawns and for the black bishop on f8 to be taken it must have been outside the pawn chain.

Just as I suspected. I presumed that the Black Bishop came out of the original square and exchanged which in fact has to be supported by proof given by zeitnotakrobat.