[Retros] Shortest At-Home Lazy-Spectators Proof Games

[Francois Labelle]

Thanks to Noam Elkies and Francois Perruchaud for their proof games. When 
I posted the challenge I already knew that 6.0 moves was impossible, and 
my computer was busy working on length 6.5. Now the computation is 
complete and here are the results.

There are exactly 16 at-home lazy-spectators PGs in 6.5 moves. They are 
all SPGs. Below I list the solutions so it's easy to see which pieces are 
doing the work (move 1), what the promotion is (move 5) and where the 
promoted piece goes (move 7).

1.a4 Nc6 2.a5 Nd4 3.a6 Nxe2 4.axb7 Nxc1 5.bxa8=R Nb3 6.R8xa7 Nxa1 7.Rxa1
1.a4 Nf6 2.a5 Ne4 3.a6 Nxd2 4.axb7 Nc4 5.bxa8=Q Nxb2 6.Qad5 Nxd1 7.Qxd1
1.a4 Nf6 2.a5 Ne4 3.a6 Nxd2 4.axb7 Ne4 5.bxa8=Q Nxf2 6.Qad5 Nxd1 7.Qxd1
1.a4 Nf6 2.a5 Ne4 3.a6 Nxd2 4.axb7 Nxb1 5.bxa8=Q Nc3 6.Qad5 Nxd1 7.Qxd1
1.a4 Nf6 2.a5 Ne4 3.a6 Nxd2 4.axb7 Nxf1 5.bxa8=Q Ne3 6.Qad5 Nxd1 7.Qxd1
1.c4 Nf6 2.c5 Ne4 3.c6 Nxd2 4.cxb7 Ne4 5.bxa8=Q Nxf2 6.Qad5 Nxd1 7.Qxd1
1.c4 Nf6 2.c5 Ne4 3.c6 Nxd2 4.cxb7 Nxf1 5.bxa8=Q Ne3 6.Qad5 Nxd1 7.Qxd1
1.f4 Nf6 2.f5 Ne4 3.f6 Nxd2 4.fxg7 Nc4 5.gxh8=Q Nxb2 6.Qhd4 Nxd1 7.Qxd1
1.f4 Nf6 2.f5 Ne4 3.f6 Nxd2 4.fxg7 Nxb1 5.gxh8=Q Nc3 6.Qhd4 Nxd1 7.Qxd1
1.f4 Nf6 2.f5 Ne4 3.f6 Nxd2 4.fxg7 Nxf1 5.gxh8=Q Ne3 6.Qhd4 Nxd1 7.Qxd1
1.h4 Nf6 2.h5 Ne4 3.h6 Nxd2 4.hxg7 Nc4 5.gxh8=Q Nxb2 6.Qhd4 Nxd1 7.Qxd1
1.h4 Nf6 2.h5 Ne4 3.h6 Nxd2 4.hxg7 Ne4 5.gxh8=Q Nxf2 6.Qhd4 Nxd1 7.Qxd1
1.h4 Nf6 2.h5 Ne4 3.h6 Nxd2 4.hxg7 Ne4 5.gxh8=R Nxf2 6.R8xh7 Nxh1 7.Rxh1
1.h4 Nf6 2.h5 Ne4 3.h6 Nxd2 4.hxg7 Nxb1 5.gxh8=Q Nc3 6.Qhd4 Nxd1 7.Qxd1 (*)
1.h4 Nf6 2.h5 Ne4 3.h6 Nxd2 4.hxg7 Nxf1 5.gxh8=Q Ne3 6.Qhd4 Nxd1 7.Qxd1
1.h4 Nf6 2.h5 Ne4 3.h6 Nxd2 4.hxg7 Nxf1 5.gxh8=R Ng3 6.R8xh7 Nxh1 7.Rxh1

(*) Francois Perruchaud's PG

Actually I got that list by improving my at-home proof game generator. 
Listing every at-home proof game in 4.0 moves now takes 14 seconds. 6.5 
moves takes a few days, and 7.0 moves would take a few weeks. The number 
of at-home proof games in 0,1,2,...,13 plies is the integer sequence

1, 0, 0, 0, 0, 0, 0, 0, 10, 41, 116, 335, 1111, 2619.

Then it was just a matter of looking for lazy-spectators proof games in 
there.

  	Francois