Meisterwerke

The inventory shows six (6) white pieces and one black knight missing. The bN has been obviously captured with f2xNe3. The unlucky position of the bBg8 and black pawn c2 indicate that this pawn has come from h7 and is accountable for the remaining 5 captures on diagonal h7-c2. Furthermore, before the last of these captures (d3xc2), the white pawn has still been at d2 and wB at c1 blocking the rook a1 from freedom. Since wK currently - after dxc2 - lives in a prison west from c1, the sixth man captured must be Ra1 heroically fallen at a1 or b1 before the d3xc2 capture.

As the white position is really bad, the only chance for a draw is to demand it based on the 50 move rule. This is the project we are set to prove.

Let us start from the fact that in order to return the current position to initial position, the white pieces must be uncaptured. This leads to the sequence of logic below, where the mark => should be read as : "But before that we must undo". Here goes:

Recover white pieces

=> d3xc2
=> d2-d3
=> Bc1 .. a7
=> b7-b6
=> Bc8...g8
=> g7-g6
=> Bf8 .. g1

before this reinstall : Rc8, Qd8,Ke8 in this order
before this bail out bQ and bR from their current prison
before this block the first rank by bringing bK to d1.

This will now form a "To Do"- list , although in reverse order, for counting moves. However we retract first the move Rc8-b8 in order to give white a chance to shuttle between a7 and b8 with his bishop. Now, playing in normal "forward" fashion and counting just black moves (white is just shuttling) until the pawn move g7-g6, we have:

Rc8 (1)
Ke8 .. g7 (2)
Bh7 (1)
Rg8 (1)
Kg7 .. Kd1 (15)
Qd2 .. h4 (2)
Bf2 (1)
Rh1 .. g3 (2)
Kd1 .. g7 (15)
Rc8 (1)
Bg8 (1)
Qh8 (1)
Bh7 (1)
Qd8 (1)
Kg7 .. e8 (2)
Rh3 (1)
Bf2 .. f8 (4)

And now undoing g7-g6 comes possible. However, summing up the moves in parenthesis gives a total of 52 moves - more than enough to claim a draw.

But why should white meekly just move the bishop? Why not undo, say somewhere around 49th retraction, a nice pawn move like g4-g5 or f2xNe3 ? (There are not others available).

The reason becomes apparent if we continue the To Do - list, until wB has been released from its prison:

Retract g7-g6
Return Bg8 to b7.

This happens in the phase when wB is at b8, losing a tempo if necessary. And now the critical phase:( As retro moves, black first)

Bb7-d5 Ba7-b8
Rb8-c8 f2xNe3
Bc8-b7 g5-g4
b6-b7 Bd4-a7 etc.

The point is that it takes two pawn moves from white to get bishop out. If white had retracted one of these pawn moves earlier, it now had to retract g4-g3 as well. But this will close the way for the Rh1 to return home after resurrection, making the position illegal. (Any hope to sneak it via f-line by retracting g5-g4-g3-g2 is lost, as f2xNe3 must be undone to return Bc1, before the rook is reborn).

This means that no pawn moves can be undone before retracting g7-g6 and as shown earlier the only capture outside c2-pawn captures and f2xe3 is the capture of Ra1 that happened before d3xc2. So, the 52-move run has indeed happened without pawn moves or captures and white can prove the 50-move draw.

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Solution by mr.mip