# [Retros] Happy New Year!

Francois Labelle flab at EECS.Berkeley.EDU
Mon Jan 19 14:31:32 EST 2004

On Fri, 16 Jan 2004, Andrew Buchanan wrote:

> It's usual practice in SPGs not to have any text e.g. "both sides can

> still castle".

I'm sorry about that. I'm a computer scientist, not an SPG composer!

But I think you noticed that it's not just any random text, it's what's
missing from the graphic to fully specify the position.

I have files containing every distinct position and the number of games
leading to it for ply 0-8. The position takes into account castling and en
passant, not by choice but by *necessity*, so that I can use the file for
ply n to generate ply n+1. I simply searched those files for "2004" and

> So what's the quickest *diagram* which can be generated by exactly 2004

> proof games? (i.e. no restriction on castling (or e.p.!)) Is there one

> in ply =< 8?

"Diagram", that's a beautiful word to explain precisely what the SPG
community wants! So I went ahead and collapsed my lists of "positions"
into lists of "diagrams".

You're going to laugh, a minor modification does the trick:

_________________

| |

| r n b q k b n r | Francois Labelle & computer

| p p p p . p p p | January 19, 2004

| . . . . p . . . |

| . . . . . . . . |

| . . . . . . . . |

| . . . . P . . P |

| P P P P . P P . | PG-3.5

| R N B Q K B N R | 2004 solutions

|_________________|

There are 4 such diagrams at ply 7 (those e-pawn can be put on e4 and e5).
There are 1664 PGs with 2004 solutions at ply 8 (871 non-shortest PGs and
793 SPGs).

The lowest n without a diagram for ply <= 8 is n=3413.
The largest n with a diagram for ply <= 8 is n=16327.

The most unsound proof game in 4.0 moves is:
_________________

| |

| r n b q k b n r | Francois Labelle & computer

| p p p . . p p p | January 19, 2004

| . . . . . . . . |

| . . . p p . . . |

| . . . P P . . . |

| . . . . . . . . |

| P P P . . P P P | PG-4.0

| R N B Q K B N R | 16327 solutions

|_________________|

Francois Labelle