s. P0000133
NN: It seems we fall short of one retro-move and fail to keep either the bK or bR still.
Let's analyse, the distribution of bPs indicate 5 captures (bPh7×g6×f5×e4×d3×c2) plus 3 captures (bPc7×d6, bPb7×c6, bg7×f6) equalling a total of 8 captures, thus accounting for all of white's missing pieces. Next, wPs captured at least 3 (fxexdxc) plus wPc2×b3. Now, in order to keep the bK & bR still, we require sufficient supply of retro-moves for black. Thus, we must strive to release the bNa1 (as pawns are not enough!) at the earliest. But this can only be done through uncapturing the bishop on c1 followed by retracting bPd3×c2, wPd2-d3. An optimal way of doing this may be: -1.bPb7×wNc6 wNc6-d4, -2.bPa4-a3 wPc6-c7, -3.bPc7×wBd6 wBd6-b4, -4.bPa5-a4 wBb4-d2 -5.bPe6-e5 wBd2-c1 and here we can't retract anymore moves without violating bK's right to castle. Retracting bPa6-a5 for instance would mean that bRa8 got out of the pawn to be captured by a wP (as bBc8 never left its homesquare) forcing the bKe8 to move.
Thus, Black can't castle and the solution is 1.Kxf6 Rh6+ (1...0-0 is illegal) 2.Nxh6 ... 3.c8R/Q# (2018-11-30)
Mario Richter: If we assume that Black can still Castle, White needs a fifth capture to provide wPh2 as a capture object.
Furthermore, before d2-d3 can be retracted, both wRa1 and wBc1 have to return home (to b1 and c1) (2018-12-01)
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