[Retros] At Home SPG-4.0

[Francois Labelle]

On Fri, 16 Jan 2004, Andrew Buchanan wrote:


> - an "at home" SPG is an SPG where all the surviving pieces are

> apparently on their start squares.  (aka "deletion", "chez soi".)

>

> - it is strongly suspected that there are no shorter deletion SPGs

> (except the trivial one at ply 0). Can you confirm this,


It's a nice problem! It wasn't hard at all to program. The word
"apparently" in the definition helped a lot.

I confirm that there are no dual-free proof games for plies 1-7. At ply 7
there are 9 proof games with multiple solutions (the minimum being 3
solutions for the empty squares b1 and d7).


> and give the list of all deletion SPGs at ply 8? That would be

> impressive.


There are 10 of them. You had #1,2,3,6,7,9,10 on your webpage, #8 is
mentioned on the solution page, #5 is CP01 from your prior art page, and
#4 is just its mirror image. (May I suggest that all 10 appear on the same
webpage?). 10/10, props to all human composers involved!


Francois Labelle & computer, January 19, 2004
All 10 "at home" SPG-4.0 (all rediscoveries)
 _________________ _________________ _________________ _________________

|                 |                 |                 |                 |

| r n . q k b n r | r n b q k b n r | r n b . k b n r | r . b q k b n r |

| p p p . p p p p | p p p . p . p p | p p . . p p p p | p p p . . p p p |

| . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . |

| . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . |

| . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . |

| . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . |

| P P P P P P P P | P P P P P P P P | P P P P P P P P | P P P P P P P P |

| R . B Q K B N R | R . B Q K B N R | R . B Q K B N R | R . B Q K B N R |

|_________________|_________________|_________________|_________________|

|                 |                 |                 |                 |

| r n b q k b . r | . n b q k b n r | r n . q k b n r | r n b q k b n r |

| p p p . . p p p | p p p p . p p p | p p p . p p p p | p p p p p p p . |

| . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . |

| . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . |

| . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . |

| . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . |

| P P P P P P P P | P P P P P P P P | P P . P P P P P | P P P P . P P P |

| R N B Q K B . R | R N B Q K B . R | R N B Q K B N R | R N B . K B N R |

|_________________|_________________|_________________|_________________|

|                 |                 |

| r n b q k b n r | r . b q k b n r |

| p p p p p p . p | p p p p p p p p |

| . . . . . . . . | . . . . . . . . |

| . . . . . . . . | . . . . . . . . |

| . . . . . . . . | . . . . . . . . |

| . . . . . . . . | . . . . . . . . |

| P P P P . P P P | P P P . P P P P |

| R N B . K B N R | R N . Q K B N R |

|_________________|_________________|



I noticed you had one SPG-4.0 with 2 solutions on your webpage. If you
open the door to those, you'd get 12 more SPGs. Allowing any number of
solutions, there are a total of 64 SPGs and 10 non-shortest PGs at ply 8.

It turns out that for an "at home" search, ply 9 and 10 are within reach.
Would that be of interest too? I'm starting the computation now. Any
guesses as to how many dual-free deletion SPGs there are at ply 9 and 10?

Cheers,

	Francois Labelle