[Retros] HAP problems up to ply 8

[Francois Labelle]

The ply 8 computation finished! To be clear, I computed HAP with "O" for 
castling, called "OHAP" by Bernd. (I see a way to do the same analysis for 
"EHAP" without recomputing everything if there's an interest.)

Number of possible HAP strings in plies 1..8:
2, 4, 15, 75, 468, 3152, 23500, 184462

The 8-ply HAP string with the most solutions:
1.P P 2.P P 3.P P 4.P P (1779740200 solutions)

Number of HAP strings that uniquely determine a game in plies 1..8:
0, 0, 0, 1, 5, 59, 341, 2652
(I'm sending files containing all these problems to Alain for his website, 
so everyone will be able to do data mining.)

Number of problems ending in checkmate:
0, 0, 0, 0, 1, 5, 25, 167

Number of problems with castling:
0, 0, 0, 0, 0, 0, 10, 170

No problem with en passant in 8 plies or less.

Solutions to the 19 black move problems that I posted:

a6: 1.e4 a6 2.Bxa6 d5 3.exd5 Qxd5 4.Bxb7
a5: 1.c4 a5 2.Nc3 a4 3.Nxa4 Rxa4 4.Qxa4
b6: 1.e3 b6 2.Qf3 Ba6 3.Qxa8 Bxf1
b5: 1.Nf3 b5 2.e3 Bb7 3.Bxb5 Bxf3
c6: 1.d3 c6 2.Bf4 Qb6 3.Bxb8 Qxf2+ 4.Kd2
c5: 1.d4 c5 2.Bf4 Qb6 3.Bxb8 cxd4
d6: 1.g4 d6 2.Bg2 Bxg4 3.Bc6+
d5: 1.Nc3 d5 2.Nxd5 Qxd5
e6: 1.b4 e6 2.Bb2 Nf6 3.Bxf6 Bxb4
e5: 1.Nf3 e5 2.Nxe5 Nc6 3.Nxc6
f6: 1.d4 f6 2.Qd3 Nc6 3.Qxh7 Nxd4 4.Qg6#
f5: 1.e4 f5 2.Qf3 fxe4 3.Qxf8+
g6: 1.d4 g6 2.Qd3 Bh6 3.Qxg6 Bxc1 4.Qxg8+
g5: 1.Nc3 g5 2.d3 Bg7 3.Bxg5 Bxc3+
h6: 1.d4 h6 2.Bxh6 f6 3.Qd3 gxh6 4.Qg6#
h5: 1.e4 h5 2.Qxh5 Nf6 3.Qxh8 Nxe4
Na6: 1.e4 Na6 2.Bxa6 d5 3.exd5 Qxd5
Nc6: 1.d4 Nc6 2.Qd3 Nxd4 3.Qf3 Nxf3+
Nf6: 1.b4 Nf6 2.Bb2 e6 3.Bxf6 Bxb4

Solution to the 20th problem by Joost/Mario:
Nh6: 1.d4 Nh6 2.Bxh6 c5 3.Bxg7 cxd4 4.Bxf8 Qa5+

 	Francois