AW: [Retros] At Home SPGs, and more

Gerd Wilts g.wilts at
Mon Feb 2 16:12:32 EST 2004

Francois Labelle wrote:



> For x=4, I get many SPG 16.5 with 3 pieces left on the board:


> 18 SPGs without Article 1.3 of the Laws

> 17 SPGs with Article 1.3 (Dead Reckoning!)


> A comment in German attached to P0005371 talks about 19 such SPGs. So

> there's a slight discrepancy here.

I checked some old documents and I found only 17 (!) such PGs (without
Article 1.3). All of them can be found on the PDB web site:

P0000245: wKg1, wQc2, bKg7
P0000370: wKd2, wQc7, bKf7
P0004246: wKf1, wQb1, bKe8
P0004247: wKc2, wRa1, bKf7
P0005389: wKf2, wPa2, bKd8
P0005394: wKc2, wRg8, bKf8
P0005395: wKd2, wBa8, bKe8
P0005396: wKe1, wRg1, bKc8
P0005397: wKd2, wRg7, bKd8
P0005398: wKg2, wPf2, bKg7
P0005399: wKf2, wBb8, bKe7 (dead reckoning!)
P0005400: wKf1, wBg5, bKf8
P0005401: wKe2, wNb1, bKc8
P0005402: wKe1, wRa2, bKd8
P0005403: wKd2, wRc7, bKf7
P0005404: wKe1, wRf2, bKd7
P0005405: wKe1, wRf7, bKe8

The first one was found by Karlheinz Bachmann. The number 19 given in the
comment to P0005371 is wrong, we (Norbert Geissler and I) had to rule out
2 of them later because of duals (our program used hash tables so we had
to check the resulting PGs for duals manually).

Does this list correspond to your list? What is the "missing" PG?

> I'm not sure yet if I can do x=5, it's really on the cutting edge of what

> I can tackle. The comment in German seems to imply that no one has done it

> before. Is it true?

x=5 has not yet been done, so there is still hope that a dualfree PG with
two Kings only exists!


Gerd Wilts

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