[Retros] No (1+1) SPG at x=5

[A J Mestel]

I'm a bit hazy on the subject, but I think the idea of the "holy grail"
was that great benefit derived from seeking it, even though it wasn't 
found. You've certainly done wonders!

   Jonathan Mestel

On Sun, 28 Mar 2004, Francois Labelle wrote:


> The month-long computer analysis of massacre proof games with 5

> non-captures (x=5) that I was running is complete. I found no proof game

> with only two kings on the board, with or without A1.3.

> 

> The best I get is one diagram with 2 solutions (with or without A1.3). I

> checked the solutions and they're almost identical, so the problem is

> cooked.

> 

> 

> For PGs with 3 units left on the board I get:

> 

> - 100 problems without A1.3

> - 13 of these are "disabled" by A1.3

> - 2 new problems are "enabled" by A1.3 (hi Andrew!)

> - for a total of 89 problems with A1.3

> (Recall that for x=4 there were 18 PGs without A1.3, and 17 PGs with

> A1.3.)

> 

> 

> I verified the two x=5 problems of the Chess Problem Database whose status

> was unknown:

> 

> P0000284 by Karlheinz Bachmann is C+ by my program

> P1000210 by Thierry Le Gleuher is C+ by my program (also C+ by Popeye

> after 46 min)

> 

> 

> Here are statistics about the interesting PGs I found along the way:

> 

> - 26170 at-home

> -   135 stalemate

> -     7 vertical symmetry with KQ-equivalent

> -  1400 horizontal symmetry and color-flip

> -   428 180-degree symmetry and color-flip

> 

> 

> Some individual SPGs of possible interest:

> 

> (1+1) in 17.5  (despite being cooked with 2 solutions)

> 

> (1+2) in 17.0  SPG enabled by A1.3 (428 solutions w/o A1.3)

> (2+1) in 17.0  "                   (6216 solutions w/o A1.3)

> 

> (7+7) in 11.5  at-home AND mirror symmetric

> (7+7) in 11.5  "

> (5+5) in 13.5  "

> (4+4) in 14.5  "

> (3+3) in 15.5  "

> 

> (3+1) in 16.5  at-home (most depleted)

> 

> (7+3) in 13.5  stalemate (least depleted)

> (1+4) in 16.0  stalemate (most depleted)

> 

> (12+10) in 7.5  vertical symmetry with KQ-equivalent

> (10+10) in 8.5  " (this one has also a variant)

> (6+8)  in 11.5  "

> (6+4)  in 13.5  "

> (4+2)  in 15.0  " (this one is x=4)

> 

> (2+2) in 16.5  180-degree symmetry and color-flip (most depleted)

> 

> 

> I didn't backtrack every solution yet. I plan to put the (1+1) problems on

> my website and post the interesting SPGs and their solutions to the

> mailing list in a few days, unless someone contacts me with a more

> glamorous publishing option. Some of the positions are pretty stunning,

> but I haven't found the "holy grail".

> 

> 	Francois

> 

> 

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