# [Retros] 1+2+3+...+63

Noam Elkies elkies at math.harvard.edu
Thu Dec 31 22:55:14 EST 2015

```Just in time:

NDE 311.xii.2015

+---a---b---c---d---e---f---g---h---+
|                                   |
8  -R  -S  -B  -S  -Q  -B   .  -R   8
|                                   |
7   .  -P   .  -P  -K  -P  -P  -P   7
|                                   |
6   .   .  -P   .  -P   .   .   .   6
|                                   |
5  -P   .   .   .   .   .   .   .   5
|                                   |
4   Q   .   .   .   .   .   .   S   4
|                                   |
3   .   P   P   .   .   P   .   .   3
|                                   |
2   P   .   .   P   P   .   P   P   2
|                                   |
1   R   S   B   .   .   B   K   R   1
|                                   |
+---a---b---c---d---e---f---g---h---+
dia8.5                    16 + 16

A) proof game in 8.5 moves; how many solutions?
B) sides reversed: proof game in 8.5; how many solutions?

Both C+ Popeye 3.41, in about 0.5 second each.

Note that neither of these is a _shortest_ proof game.

Position A is

Pieces  White  Ra1 Sb1 Bc1 Qa4 Kg1 Bf1 Sh4 Rh1 Pa2 Pb3 Pc3 Pd2 Pe2 Pf3 Pg2 Ph2
Black  Ra8 Sb8 Bc8 Qe8 Ke7 Bf8 Sd8 Rh8 Pa5 Pb7 Pc6 Pd7 Pe6 Pf7 Pg7 Ph7
http://www.janko.at/Retros/d.php?ff=rnbnqb1r/1p1pkppp/2p1p3/p7/Q6N/1PP2P2/P2PP1PP/RNB2BKR

Position B is
Pieces  White  Ra1 Sb1 Bc1 Qe1 Ke2 Bf1 Sd1 Rh1 Pa4 Pb2 Pc3 Pd2 Pe3 Pf2 Pg2 Ph2
Black  Ra8 Sb8 Bc8 Qa5 Kg8 Bf8 Sh5 Rh8 Pa7 Pb6 Pc6 Pd7 Pe7 Pf6 Pg7 Ph7
http://www.janko.at/Retros/d.php?ff=rnb2bkr/p2pp1pp/1pp2p2/q6n/P7/2P1P3/1P1PKPPP/RNBNQB1R

Happy New Year!
--Noam D. Elkies
```