Hardest Mate in 4 of All Time

1. Qh3 Kd8 2. b7 b4 3. Qxh6 gxh6 4. b8#
1. Qh3 Kd8 2. b7 b4 3. Qxh6 Rxh6 4. b8#
1. Qh3 Kd8 2. b7 b4 3. Qxh6 C4 4. b8#
1. Qh3 Kd8 2. b7 b4 3. Qxh6 f5 4. b8#
1. Qh3 Kd8 2. b7 b4 3. Qxh6 Ke8 4. b8#
1. Qh3 Kd8 2. b7 c4 3. Qxh6 gxh6 4. b8#
1. Qh3 Kd8 2. b7 c4 3. Qxh6 Rxh6 4. b8#
1. Qh3 Kd8 2. b7 c4 3. Qxh6 b4 4. b8#
1. Qh3 Kd8 2. b7 c4 3. Qxh6 f5 4. b8#
1. Qh3 Kd8 2. b7 c4 3. Qxh6 Ke8 4. b8#
1. Qh3 Kd8 2. b7 f5 3. Qxh6 gxh6 4. b8#
1. Qh3 Kd8 2. b7 f5 3. Qxh6 Rxh6 4. b8#
1. Qh3 Kd8 2. b7 f5 3. Qxh6 b4 4. b8#
1. Qh3 Kd8 2. b7 f5 3. Qxh6 c4 4. b8#
1. Qh3 Kd8 2. b7 f5 3. Qxh6 Ke8 4. b8#
1. Qh3 Kd8 2. b7 h5 3. Qxh5 Rxh5 4. b8#
1. Qh3 Kd8 2. b7 h5 3. Qxh5 b4 4. b8#
1. Qh3 Kd8 2. b7 h5 3. Qxh5 c4 4. b8#
1. Qh3 Kd8 2. b7 h5 3. Qxh5 f5 4. b8#
1. Qh3 Kd8 2. b7 h5 3. Qxh5 Ke8 4. b8#
1. Qh3 Kd8 2. b7 Re8 3. Kd1 b4 4. b8#
1. Qh3 Kd8 2. b7 Re8 3. Kd1 C4 4. b8#
1. Qh3 Kd8 2. b7 Re8 3. Kd1 f5 4. b8#
1. Qh3 Kd8 2. b7 Re8 3. Kd1 h5 4. b8#
1. Qh3 Kd8 2. b7 Re8 3. Kd1 Rf8 4. b8#
1. Qh3 Kd8 2. b7 Re8 3. Kd1 Rg8 4. b8#
1. Qh3 Kd8 2. b7 Re8 3. Kd1 Rh8 4. b8#
1. Qh3 Kd8 2. b7 Re8 3. Kd1 Rxe3 4. b8#
1. Qh3 Kd8 2. b7 Rf8 3. Qxh6 gxh6 4. b8#
1. Qh3 Kd8 2. b7 Rf8 3. Qxh6 b4 4. b8#
1. Qh3 Kd8 2. b7 Rf8 3. Qxh6 c4 4. b8#
1. Qh3 Kd8 2. b7 Rf8 3. Qxh6 f5 4. b8#
1. Qh3 Kd8 2. b7 Rf8 3. Qxh6 Ke8 4. b8#
1. Qh3 Kd8 2. b7 Rg8 3. Qxh6 gxh6 4. b8#
1. Qh3 Kd8 2. b7 Rg8 3. Qxh6 b4 4. b8#
1. Qh3 Kd8 2. b7 Rg8 3. Qxh6 c4 4. b8#
1. Qh3 Kd8 2. b7 Rg8 3. Qxh6 f5 4. b8#
1. Qh3 Kd8 2. b7 Rg8 3. Qxh6 Ke8 4. b8#
1. Qh3 Kf8 2. b7 b4 3. Qxd7 c4 4. b8#
1. Qh3 Kf8 2. b7 b4 3. Qxd7 f5 4. b8#
1. Qh3 Kf8 2. b7 b4 3. Qxd7 h5 4. b8#
1. Qh3 Kf8 2. b7 b4 3. Qxd7 Rg8 4. b8#
1. Qh3 Kf8 2. b7 c4 3. Qxd7 b4 6 4. b8#
1. Qh3 Kf8 2. b7 c4 3. Qxd7 f5 4. b8#
1. Qh3 Kf8 2. b7 c4 3. Qxd7 h5 4. b8#
1. Qh3 Kf8 2. b7 c4 3. Qxd7 Rg8 4. b8#
1. Qh3 Kf8 2. b7 f5 3. Qxf5 Ke8 4. b8#
1. Qh3 Kf8 2. b7 f5 3. Qxf5 Kg8 4. b8#
1. Qh3 Kf8 2. b7 f5 3. Qxf5 Kg8 4. Qf7#
1. Qh3 Kf8 2. b7 h5 3. Qxh5 Rxh5 4. b8#
1. Qh3 Kf8 2. b7 h5 3. Qxh5 Rg8 4. b8#
1. Qh3 Kf8 2. b7 h5 3. Qxh5 b4 4. b8#
1. Qh3 Kf8 2. b7 h5 3. Qxh5 c4 4. b8#
1. Qh3 Kf8 2. b7 h5 3. Qxh5 f5 4. b8#
1. Qh3 Kf8 2. b7 h5 3. Qxh5 Ke8 4. b8#
1. Qh3 Kf8 2. b7 Rg8 3. Qxh6 gxh6 4. b8#
1. Qh3 Kf8 2. b7 Rg8 3. Qxd7 b4 4. b8#
1. Qh3 Kf8 2. b7 Rg8 3. Qxd7 b4 4. Qf7#
1. Qh3 Kf8 2. b7 Rg8 3. Qxd7 C4 4. b8#
1. Qh3 Kf8 2. b7 Rg8 3. Qxd7 C4 4. Qf7#
1. Qh3 Kf8 2. b7 Rg8 3. Qxd7 f5 4. b8#
1. Qh3 Kf8 2. b7 Rg8 3. Qxd7 f5 4. Qf7#
1. Qh3 Kf8 2. b7 Rg8 3. Qxd7 h5 4. b8#
1. Qh3 Kf8 2. b7 Rg8 3. Qxd7 h5 4. Qf7#
1. Qh3 Rf8 2. b7 Rg8 3. Qxh6 gxh6 4. b8#
1. Qh3 Rf8 2. b7 Rh8 3. Qxh6 gxh6 4. b8#
1. Qh3 Rf8 2. b7 Rh8 3. Qxh6 Rxh6 4. b8#
1. Qh3 Rf8 2. b7 Kd8 3. Qxh6 gxh6 4. b8#
1. Qh3 Rf8 2. b7 b4 3. Qxh6 gxh6 4. b8#
1. Qh3 Rf8 2. b7 c4 3. Qxh6 gxh6 4. b8#
1. Qh3 Rf8 2. b7 f5 3. Qxh6 gxh6 4. b8#
1. Qh3 Rf8 2. b7 f5 3. Qxf5 b4 4. b8#
1. Qh3 Rf8 2. b7 f5 3. Qxf5 c4 4. b8#
1. Qh3 Rf8 2. b7 f5 3. Qxf5 h5 4. b8#
1. Qh3 Rf8 2. b7 f5 3. Qxf5 Rxf5 4. b8#
1. Qh3 Rf8 2. b7 f5 3. Qxf5 Rg8 4. b8#
1. Qh3 Rf8 2. b7 f5 3. Qxf5 Rh8 4. b8#
1. Qh3 Rf8 2. b7 h5 3. Qxh5 Rxh5 4. b8#
1. Qh3 Rg8 2. b7 Rf8 3. Qxh6 gxh6 4. b8#
1. Qh3 Rg8 2. b7 Rh8 3. Qxh6 gxh6 4. b8#
1. Qh3 Rg8 2. b7 Kd8 3. Qxh6 gxh6 4. b8#
1. Qh3 Rg8 2. b7 b4 3. Qxh6 gxh6 4. b8#
1. Qh3 Rg8 2. b7 c4 3. Qxh6 gxh6 4. b8#
1. Qh3 Rg8 2. b7 f5 3. Qxh6 gxh6 4. b8#
1. Qh3 Rg8 2. b7 h5 3. Qxh5 Rxh5 4. b8#
1. Qh3 b4 2. b7 Kd8 3. Qxh6 gxh6 4. b8#
1. Qh3 b4 2. b7 Kd8 3. Qxh6 c4 4. b8#
1. Qh3 b4 2. b7 Kd8 3. Qxh6 f5 4. b8#
1. Qh3 b4 2. b7 Kd8 3. Qxh6 Rxh6 4. b8#
1. Qh3 c4 2. b7 Kd8 3. Qxh6 gxh6 4. b8#
1. Qh3 c4 2. b7 Kd8 3. Qxh6 b4 4. b8#
1. Qh3 c4 2. b7 Kd8 3. Qxh6 f5 4. b8#
1. Qh3 c4 2. b7 Kd8 3. Qxh6 Rxh6 4. b8#
1. Qh3 f5 2. b7 Kd8 3. Qxh6 gxh6 4. b8#
1. Qh3 f5 2. b7 Kf8 3. Qxf5 Ke8 4. b8#
1. Qh3 f5 2. b7 Kf8 3. Qxf5 Kg8 4. b8#
1. Qh3 f5 2. b7 Kf8 3. Qxf5 Kg8 4. Qf7#
1. Qh3 h5 2. b7 Kd8 3. Qxh5 Ke8 4. b8#
1. Qh3 h5 2. b7 Kd8 3. Qxh5 Rxh5 4. b8#
1. Qh3 h5 2. b7 Kd8 3. Qxh5 b4 4. b8#
1. Qh3 h5 2. b7 Kd8 3. Qxh5 c4 4. b8#
1. Qh3 h5 2. b7 Kd8 3. Qxh5 f5 4. b8#
1. Qh3 h5 2. b7 Kd8 3. Qxh5 Rf8 4. b8#
1. Qh3 h5 2. b7 Kd8 3. Qxh5 Rg8 4. b8#
1. Qh3 b4 2. b7 Kf8 3. Qxd7 Rg8 4. b8#
1. Qh3 b4 2. b7 Kf8 3. Qxd7 C4 4. b8#
1. Qh3 b4 2. b7 Kf8 3. Qxd7 f5 4. b8#
1. Qh3 b4 2. b7 Kf8 3. Qxd7 h5 4. b8#
1. Qh3 b4 2. b7 Kf8 3. Qxd7 Kg8 4. b8#
1. Qh3 b4 2. b7 Kf8 3. Qxd7 Kg8 4. Qf7#
1. Qh3 c4 2. b7 Kf8 3. Qxd7 b4 4. b8#
1. Qh3 c4 2. b7 Kf8 3. Qxd7 f5 4. b8#
1. Qh3 c4 2. b7 Kf8 3. Qxd7 h5 4. b8#
1. Qh3 c4 2. b7 Kf8 3. Qxd7 Rg8 4. b8#
1. Qh3 h5 2. b7 Kf8 3. Qxh5 Ke8 4. b8#
1. Qh3 h5 2. b7 Kf8 3. Qxh5 Ke8 4. Qxh8#
1. Qh3 h5 2. b7 Kf8 3. Qxh5 Rxh5 4. b8#
1. Qh3 h5 2. b7 Kf8 3. Qxh5 b4 4. b8#
1. Qh3 h5 2. b7 Kf8 3. Qxh5 b4 4. Qxh8#
1. Qh3 h5 2. b7 Kf8 3. Qxh5 c4 4. b8#
1. Qh3 h5 2. b7 Kf8 3. Qxh5 c4 4. Qxh8#
1. Qh3 h5 2. b7 Kf8 3. Qxh5 f5 4. b8#
1. Qh3 h5 2. b7 Kf8 3. Qxh5 f5 4. Qxh8#
1. Qh3 h5 2. b7 Kf8 3. Qxh5 Rg8 4. b8#
1. Qh3 h5 2. b7 Kf8 3. Qxd7 b4 4. b8#
1. Qh3 h5 2. b7 Kf8 3. Qxd7 b4 4. Qf7#
1. Qh3 h5 2. b7 Kf8 3. Qxd7 c4 4. b8#
1. Qh3 h5 2. b7 Kf8 3. Qxd7 c4 4. Qf7#
1. Qh3 h5 2. b7 Kf8 3. Qxd7 f5 4. b8#
1. Qh3 h5 2. b7 Kf8 3. Qxd7 f5 4. Qf7#
1. Qh3 h5 2. b7 Kf8 3. Qxd7 Kg8 4. b8#
1. Qh3 h5 2. b7 Kf8 3. Qxd7 Kg8 4. Qf7#

In the FEN and PGN posted, noone can castle.

 If I fix that then in reply to bookkeyper's variation:

1. Qh3 b4 2. b7 O-O

Black castled in response to b7. Your variations don't cover that.

If the FEN/PGN is correct and Black cannot castle, then Stockfish finds a forced mate in 2.

[M2]  1.b7 Kd8 2.b8=Q#

I'll solve it.

1. Qc4! preventing castling this move. 1...bxc4 2. 0-0! and black permanently cannot castle. 3. b7 and 4. b8=Q/R# unstoppable. Sidelines 1...anything else 2. b7 and 3. b8=Q/R# mates.

It's obvious why 1. Qc4 prevents castling, but why 2. 0-0? Simple.

White is missing P, 2B, R, black missing 7 units. Assume white can castle. The Bc1 died at home, the wRa1 couldn't have escaped, therefore black's 2 pawn captures axb and bxc captured wBf1 and another unit. This means that white must have promoted a pawn. White needs 5 captures for the pawn structure on the board, and which leaves 2 captures for the promotion; whatever we try, the pawn promoted either on h8 (bR has moved) or f8 (passing by f7, bK has moved) and black can't castle.

PRA convention: Castling is legal unless proven otherwise. White's 2. 0-0 is legal by "benefit of doubt" so to speak, whereupon black's ...0-0 is provably illegal, and white mates by promotion.

Honestly not a hard problem by retro standards, but I don't particularly like bashing my head against some of the more nightmarish ones, so this was quite enjoyable.

EDIT: I see caveatcanis already solved it in #10 and #13. As expected. :-)

No clue...I'm a dunderhead at retrograde analysis. 

Why assume anything? If you check out the FEN then you'll see that no side can castle. So unless the OP made a mistake with this puzzle, no side can castle.

FEN's definition of "a position" includes castling rights.

For retro problems, that's an over-specfication. You're shown the position on the board but you have to infer castling rights.

The position shown on the board could potentially correspond to 4 different FEN's (White can castle, Black can castle, neither can castle or both can castle), except that the last one is provably impossible - and the proof is the core of the puzzle.

The OP had to post some FEN, but there's no one FEN that works properly for this  class of retro puzzle,

Guys did you actually can see a mate in 5 moves, witch includes black castling? 

If don't I can say I see it and it not including whites castling or promotion...

The poster of the puzzle should infer castling rights, depending on where he saw the puzzle and on what the actual solution is. So I am waiting for the OP to specify the castling rights.

What if Black does 1 ... b4

What is Black plays 3. ... Rg8?

1. Nf5 O-O 2.Qe2 Kh8 3.Qe7 Rg8 4.Rxh6+ gxh6 5.Qh7#

So we agree that there are some forced mates in 5? 

I am waiting for the OP to post a forced mate in 4 solution.

i think its possible to construct a theoretical game (reaching problem position, from stating position) where both white & black can castle.

hence M4 not possible, 1.Qc4 bxc4 2.O-O O-O 

What is the black last move!

I am interested in puzzles that are difficult for engines but the OP has not cleared up the confusion about castling rights and has not confirmed a forced mate in 4.

I believe this is a forced mate in 5 which takes just a few seconds for Stockfish to find.  Disappointing

(Although I didn't let Stockfish run for more than a minute, just to be clear.)

We were promised a mind-blowing solution with mate in 4, will the OP deliver? Or is it a non-forced mate in 4, easily refutable by engines?

The suspense!

Try it. It shouldn't work.

Chess puzzles are not a religion and you need not wait for a message  from heaven. The very simple solution is clearly explained by Remellion.

The perceived mystery around this puzzle type has nothing to do with its difficulty but with the lack of knowledge and understanding of the retrograde logic supporting it. It cannot be solved with just standard deterministic chess rules but needs additional 'conventions' handling the 'missing information'. One of them is the 'castling right', the other one is about arbitrating between 'clashing castling rights'. With these conventions in place, the puzzle solution is correct.