N.Hoeg : White retracts a move and mates in 1. White missing pcs: B,B,N,N,Pf,Pg,Ph = 7 Black missing pcs:  N = 1 Captures: White has captured a knight with so far unspecified way. Black has made following pawn captures: * e7xd6xc5xb4xa3 (4 captures) * a7xb6 or a6xb5 (1 capture) Note that none of the pawns Pf,Pg,Ph could be captured here because they cannot 'reach' this zone. In addition, since 7 white men are missing, there has been two more so far unspecified black captures.

The Analysis of the queenside:  There appears to be a very tight  prison in the North-West corner. This prison only opens after retraction
of the key move b2-b4. Then Ka4,Qa5,Ra6 and Nb8 can easily be released. However, if the a-pawn capture was a6xb5, we find that wKa8
is still confined in an unbreakable cage. Therefore this capture must have been a7xb6 (while Ba7 was on b8), when Rb7,Rc7 can be released
via b6, Bb8 via d6-f8 and finally the Ka8 following bishop's route.
Now all  queenside pawn captures have happened on  dark squares, so Bf1 cannot be one of the targets. Also all of these captures have
happened before b2-b4 released the Bc1. Hence this bishop was not among queenside captured men. It follows that 5 white pieces captured
on 5 dark queenside squares must have been  white Q,N,N and two promoted pieces (say queens) from missing f..h pawns. As there is Qh1
in the final position, this must be in fact promoted from the third kingside pawn. So all three white pawns just walked through the  opposing
black pawns and promoted. Well, perhaps this needs a closer look :)

The Analysis of the kingside: How do you get 3 white pawns to bypass 3 opposing black pawns and leave the black formation untouched?
The only way for opposing pawns to bypass each other is that one of the pawns captures something. For three side by side pawns to bypass
you need (at least) three captures. Luckily we learned from the 'Captures' above that there are exactly three unspecified captures available.
Only they are not so unspecified any more. We can now  identify these captures :
* A black pawn on f-h file will capture the Bf1 so that opposing white pawn will queen.
* A white pawn will capture the black knight in a way that enables the capturing pawn to promote.
* The black pawn blocking the last white pawn will capture the Bc1 and  give way to the promotion of the third white pawn.
Although we do not yet know the precise squares where these captures happen, we now have a general schema  of the kingside events.
Because the formation of the black pawns is the same before and after bypass, we can be a bit more specific. Two of the black pawns must
have cross-captured the white bishops, ie fxg+gxf or hxg+gxh. Further we know that two of the captures happened before critical b2-b4 and
one -that of Bc1- was the last capture.The white pawn freed by the last capture proceeded to queen and now poses as Qh1. Now we are in
position to give even more detailed analysis of what happened on king side:
(1) A black pawn captured Bf1 on a square that took it behind the white pawn chain and the opposing white pawn queened.
(2) A white f- or h-pawn , not opposing the cross-capturing black pawn pair, captured the bN in a way that enabled it to queen.
(3) Remaining white pawn was pushed as far as possible, while black pawns were kept as far back as possible.
(4) The two new queens were  captured by c5xb4 and b4xa3.
(5) Immediately after b4xa3 white moves b2-b4  that releases Ra1 and Bc1. Ra1 is taken to back row and Bc1 to kingside for capture.
(6) The remaining blocked black pawn captures the Bc1.
(7) The single white pawn, released by the last black capture, marches to queen and further to h1.
(8) Sometime after b2-b4, but not as last move, white takes time to move c2-c3.
In the critical position-after b2-b4 by white- black will have only pawn moves until they rest side-by-side on the second rank. As white has
a lot to do (5...8) it makes sense to do (3), while there is time. Note also that  (1) and (2) can be done in opposite order.

Systematic analysis of the kingside pawn captures: All the above was the proverbial 1% of inspiration. It is time for 99% of perspiration.
Starting from an intermediate position, where  the whole procedure (1...8 ) is undone, we examine all possible captiures of Bf1 until we have
the solution. In this intermediate position (until pos.5 above) both parties have tempos (w:Ra1-b1, bKa4-b4). Note also that at least one of the
white pawns must be on 4th rank to allow Rh1 to go to a6. All the analysis with comments is animated  here .

The solution is: White retracts Rh8-d8 and instead mates with Qh1-d1#   Back