[Retros] At home proof games in 7.0 moves

Francois Labelle flab at EECS.Berkeley.EDU
Mon Feb 7 02:19:25 EST 2005

Noam Elkies wrote:

> The castling problems are particularly lovely.

Thanks. I liked them too, but didn't imagine they were that good. I
thought that the castling had to be completely invisible for a castling
problem to be good.

> The 4.5/5.5 move PG is neat too; pity about the transposition dual that

> prevents the 4.5 move solution from being unique as well. There's a

> locally unique sequence in 6.0 as well, 1 d4 Nc6 2 Qd2 N:d4 3 Qh6 Ne6 4

> f4 N:f4 5 B:f4 N:h6 6 B:c1 Ng8, but it can't be unique or Francois would

> have found it as a min+1.5 PG.

Right. For that PG, the number of solutions in 8-14 plies is the sequence

0 2 0 1 180 28076 12405.

> Short of manually going through all 124 of these, maybe the computer

> could be asked whether any of them have no moves in common between the

> two solutions, or failing that which of the 124 minimize the number of

> shared moves.

Well, I'm sending them to the multiple-solution department, Joost de Heer,
for analysis.

Mario Richter wrote:

> It would be interesting for me to know how long you needed to complete

> the search and what exactly is the output of your program (obviously the

> final positions + some extra info, e.g. that a castling occurred - but

> what exactly do you keep track of?)

It took 50 days and 40 GB of temporary disk space on a 800 MHz machine,
but I don't claim that it *needed* that much. I used a simple kind of
pruning so that I'd be convinced that the results are correct. Now I can
try 7.0 again with a smarter pruning strategy to debug it, and then maybe
7.5 can be done.

I count the number of solutions of every goal diagram that can be obtained
(in this case "at-home" diagrams in 7.0 moves or less). This reminds me...

Happy New Year at home! (a bit late)
SPG in 7.0 moves, how many solutions?

And nowadays I keep track of the solutions for the problems that have 1,2
or 3 solutions. Note that the solutions could instead be found by a proof
game solver afterwards, but in general that's a bad idea because sometimes
my computer comes up with tough problems.


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