# A nice retro problem

David113
Posers and Puzzles 27 Aug '06 10:21
1. 27 Aug '06 10:21

Which white man was captured on d6? which on e6? which on f6, and which on g6?
2. BigDoggProblem
27 Aug '06 20:083 edits
Originally posted by David113

Which white man was captured on d6? which on e6? which on f6, and which on g6?[/b]
Black captured all 4 missing White units with pawns.

White can't retract -1.Rb7xb8+, because the NW corner can't be unlocked. Instead, he must try -1.a7xb8=R, which means he captured Black's 7 missing units with pawns (a7=f2).

bBc8 could only have been captured on b3 (all other wP caps are on dark squares). But if this is done immediately, there are problems getting a Rook home to a8. Indeed, the only way to make sure Ra8 can get home is to not uncapture a Black pawn on a7. This means that the a7 pawn must have promoted, for there is no other way to get it captured.

-1.a7xNb8=R Nc6-b8 -2.Qa6-c8 Ne5-c6 -3.Kc8-c7 Nd3-e5 -4.Bc7-d8 Nc5-d3 -5.Bb8-c7 c7xBd6

A surprise. The bN is the only piece that can unpromote on a1, but it must wait until wBc1 gets home. Since Bb8 can't yet get out of NW corner, Black must provide a 2nd Bishop to return to c1.

-6.Be5-d6 Nd3-c5 -7.Nc4-b2 Nc5-d3 -8.Bb2-e5 Nd3-c5 -9.Bc1-b2 Nc5-d3 -10.b2-b3 Nb3-c5 -11.Bf7-e8 Na1-b3 -12.Bg8-f7 f7xRe6

This R is needed to return home to a1 before a2xBb3 is retracted. It must come from e6, since gxRf6 isn't possible because Bf8's not home, and hxRg6 isn't possible because the wPh hasn't yet unpromoted.

-13.Re3-e6 a2-a1=N -14.Nd4-b5 a3-a2 -15.Kd8-c8 a4-a3 -16.Ra3-e3 Kb7-a8 -17.Qb5-a6 Ka8-b7 -18.b3-b4 Bb4-a5 -19.Ra1-a3 Bd6-b4 -20.a2xBb3 Kb7-a8 -21.Ke8-d8 Kc8-b7 -22.Kf8-e8 Kd8-c8 -23.Na3-c4 Bd5-b3 -24.~ Bb7-d5 -25.~ Bc8-b7 -26.~ b7-b6 -27.b6xRa7 etc.

wBb8 makes its way to h8 and unpromotes, then wBg8 unpromotes (no other way to escape!).

White's Bf1 was captured on g6 (light square), and so by elimination, wRh1 was captured on f6.
3. 27 Aug '06 20:38
Correct ðŸ™‚