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
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
=> Bc1 .. a7
=> 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:
Ke8 .. g7 (2)
Kg7 .. Kd1 (15)
Qd2 .. h4 (2)
Rh1 .. g3 (2)
Kd1 .. g7 (15)
Kg7 .. e8 (2)
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
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:
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)
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.
Solution by mr.mip