# [Retros] SPGs enabled by A1.3

Francois Labelle flab at EECS.Berkeley.EDU
Sat May 1 22:01:20 EDT 2004

After a complete analysis of my x=5 massacre data, I found a total of 10
PGs enabled by Article 1.3:

4 PGs depend on insufficient material
6 PGs depend on a forced stalemate

Here's one example of each type. For each example I give the diagram, and
two diagrams one ply before to show the A1.3-legal move and the
A1.3-illegal move.

1)
_________________ _________________ _________________

| | | |

| . . . k . b . . | . . . R k b . . | . . . . . b . . | a) SPG in 17.0

| . . . . . . . . | . . . . . . . . | . . . k . . . . |

| . . . . . . . . | . . . . . . . . | . . . . . . . . | one ply before:

| . . . . . . . . | . . . . . . . . | . . . . . . . . | b) 1 solution

| . . . . . . . . | . . . . . . . . | . . . . . . . . | c) 427 solutions

| . . . . K . . . | . . . . K . . . | . . . . K . . . |

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

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

|_________________|_________________|_________________|

Solution:
1. d4 e5 2. Bf4 exd4 3. Bxc7 Qxc7 4. Qxd4 Qxh2 5. Qxg7 Qxg1 6. Qxg8 Rxg8 7.
Rxh7 Rxg2 8. Rxf7 Rxf2 9. Rxd7 Rxe2+ 10. Kxe2 Qxf1+ 11. Ke3 Qxb1 12. Rxb7
Qxa2 13. Rxb8 Qxb2 14. Rxa7 Qxc2 15. Rxc8+ Qxc8 16. Rxa8 Qd8 17. Rxd8+
Kxd8

Forbidden solutions (one of them):
1. d4 e5 2. Bf4 exd4 3. Bxc7 Qxc7 4. Qxd4 Qxh2 5. Qxa7 Qxg1 6. Qxb8 Qxf2+
7. Kxf2 Rxa2 8. Qxb7 Rxa1 9. Rxh7 Rxb1 10. Rxh8 Rxb2 11. Rxg8 Rxc2 12. Rxg7
Bxb7 13. Rxf7 Bxg2 14. Rxd7 Bxf1 15. Kxf1 Rxe2 16. Kxe2 Kxd7 17. Ke3 Kd8

2)
_________________ _________________ _________________

| | | |

| . . . . k . . . | . . . . k . . . | . . . . k . . . | a) SPG in 15.5

| Q . . . B . . . | r Q . . B . . . | Q . . . B . . . |

| . . . . . . . . | . . . . . . . . | . . . . . . . . | one ply before:

| . . . . . . . . | . . . . . . . . | . . . . . . . . | b) 1 solution

| . . . . . . . . | . . . . . . . . | . . . . . . . . | c) 32 solutions

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

| . . . . K . . . | . . . . K . . . | . . . . q . . . |

| . . . . . R N . | . . . . . R N . | . . . . K R N . |

|_________________|_________________|_________________|

Solution:
1. d4 Nh6 2. Bxh6 d6 3. Bxg7 Be6 4. Bxf8 Bxa2 5. Bxe7 Bxb1 6. Rxa7 Bxc2 7.
Qxc2 Rg8 8. Qxc7 Rxg2 9. Qxd6 Rxh2 10. Qxb8 Rxf2 11. Qxb7 Qxd4 12. Rxh7
Qxb2 13. Rxf7 Rxf1+ 14. Rxf1 Qxe2+ 15. Kxe2 Rxa7 16. Qxa7

Forbidden solutions (one of them):
1. d4 Nh6 2. Bxh6 d6 3. Bxg7 Be6 4. Bxf8 Bxa2 5. Bxe7 Bxb1 6. Rxa7 Bxc2 7.
Qxc2 Rxa7 8. Qxc7 Rg8 9. Qxd6 Rxg2 10. Qxb8 Rxh2 11. Qxb7 Rxf2 12. Qxa7
Qxd4 13. Rxh7 Qxb2 14. Rxf7 Rxf1+ 15. Rxf1 Qxe2+ 16. Kxe2

REPLIES

Michel Caillaud wrote:

> R143 is "humanly" very difficult, and I think it can't be solved except

> investing enormous time (which I will not try).

Maybe it's still possible to have fun with massacre PGs by asking a friend
to play half of the moves for you (or 1/3 or 2/3 depending on taste). Then
you get two manageable sub-PGs: reaching the intermediate position, and
reaching the final position from the intermediate position.

> Well, we cannot be absolutely sure that there are not undiscovered bugs

> in Popeye, Natch or Euclide (and indeed some were found in the past),

> nevertheless problems tested by them are admitted "C+".

The difference is that my program's purpose isn't to test, but to compose
problems. The code in these other programs is stabilized, while my code
keeps changing depending on which kind of problem I want to compose.
Running it is also more complicated.

To decide what to do, first we can look at the precedents. Were the
Wilts/Geissler massacres published as C+?

Personally I think that the proper way to phrase it would be to list
"computer" as a co-author, because in this case its contribution is so
important. This would tell people that the problem is almost certainly
correct, and help explain how someone could possibly come up with this
stuff. But according to the precedents this isn't done.

> Until now, your programming has proved rather performing, what gives a

> high level of confidence in your results.

Yes, I'd say that R143 is about 96% certain, and 98% if it survives a
simple manual check for duals. People shouldn't waste time trying to find
a cook.

Andrew Buchanan wrote:

> As far as the Holy Grail is concerned, the hope is still out there for

> the next generation to explore x=6.

It might be possible to check x>=6 faster by constraining the search to
promising king positions only. I hope I have time to try this over the
summer.

Francois