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MatPlus.Net Forum General Illegal Symmetric double stalemate with all pieces
 
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(1) Posted by Hauke Reddmann [Friday, Jan 7, 2022 17:17]

Illegal Symmetric double stalemate with all pieces


Surely this has been done wayyyy back?
(Wayyyy = I did one 1975, but expect 1875 :-)

Of course I'd like to see a "only mildly illegal" :-)
(counting the impossible pawn captures,
otherwise you could e.g. pile up Black on White's 1st
and vice versa).
 
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(2) Posted by Joose Norri [Saturday, Jan 8, 2022 13:52]

Surely the search must start with Dawson's Five Classics of Fairy Chess and Fabel's books. I'll report later today...
 
 
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(3) Posted by Hauke Reddmann [Saturday, Jan 8, 2022 14:23]

THX! Here is mine, with four impossible pawn captures each:

(= 16+16 )

 
   
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(4) Posted by Joose Norri [Sunday, Jan 9, 2022 20:44]

Reichhelm didn't quite have the guts 140 years ago, see P0002838. I think it's fair to say many people have noticed the possibilities of the position...
 
   
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(5) Posted by Andrew Buchanan [Monday, Jan 10, 2022 10:47]

Reichhelm's fine P0002838 is:

(= 15+15 )

It appears in PDB with the comment:
 QUOTE 
"30 (the most possible) men in legal position with no move" TRD, Ultimate Themes

But TRD's remark is no longer true! Repurposing a problem I made earlier (P1346927):

(= 16+16 )

with 32 units.
If White is to move, then the position is dead. 1.fxg6ep? is illegal because f8 cannot have been retro-blocked.
If Black is to move, then we require the e.p. convention to tell us that neither 1.bxa3ep? nor 1.bxc3ep? are permitted, so Black is pat.

That's enough for me, but you may want something even more precise to eliminate the slightest possibility of Black moving. Then repurpose P1346926:

(= 15+16 )

with 31 units (wPg was waylaid to clear the route for bPg promotion).
Again with White to move, the position is dead, while with Black to move, the position is stalemate.
With WTM, the prior move can only have been R:1.b4-b3 eschewing a life-giving e.p. that must necessarily have been available.
 
   
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(6) Posted by Hauke Reddmann [Monday, Jan 10, 2022 17:35]

Andrew cheats again :-) But if you utilize "dead", what hinders
one to do something like this?

(= 16+16 )

 
   
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(7) Posted by Andrew Buchanan [Monday, Jan 10, 2022 19:41]

Hi Hauke - yours is another perfectly reasonable arrangement of the White material which is under-determined in this matrix. What's your objective in sticking some of the White officers in a corner? I kind of liked the arrangement I'd got where the white officers are able to gambol free, and wSe3 carefully blocks a lot of otherwise life-giving moves.
 
   
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(8) Posted by Joose Norri [Monday, Jan 10, 2022 21:42]

And compare your positions with P1106809 and others by Fielder.
 
   
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(9) Posted by Andrew Buchanan [Tuesday, Jan 11, 2022 03:40]

Of the prior art, there's one which is really cool:

P1182050 Thomas R. Dawson - The Chess Amateur 1923
(= 16+16 )

Only 2 moves with 32 pieces

So under the Dead Position rule, this now is a two-sided drawn position. In the other positions of this type in PDB, an allowable move can open up the game again, but not this one. The position is not entirely unique, as QR can be transposed for either side. The g-file pawn pair is also somewhat flexible in location. There is also mention of a mysterious position by P.Frey, but I don't know if it was ever published.

If I was doing this, I would aim to *maximize* the number of White moves that fail to relieve the looming stalemate, and also shift g-file pawn pair for e.p. try merriment (which TRD excludes explicitly in his task). Hence the following construction: White has 39 moves that fail to resuscitate the game, and 2 e.p. tries which fail due to f8. Such construction problems are all about legality, so are best classified as retro genre (not "fairy" or "mathematics") so Dead Position rule would apply under Article 17A, even without the e.p. angle.

after T.R.Dawson
SCHEMA!
(= 16+16 )

Duplex drawn position with 32 pieces

Following discussions with Christian Poisson, the magic word "Schema" will indicate that a diagram is not for the database. My own internal term for a problem which is self-published (or published) but has no business being in a database is "Meh!" So this is "Sche-meh!"
 
   
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(10) Posted by Hauke Reddmann [Tuesday, Jan 11, 2022 09:45]

wQd1,Ra2,Rg2,Kh8 gives 40, methinks. (Kg7 41, but if you want
to keep the ep tries...)
 
   
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(11) Posted by Andrew Buchanan [Tuesday, Jan 11, 2022 10:07]

Hi, Hauke,

I knew that whatever number I put in, you would do better :-) However fortunately for my pride, one can do better still for 42+2. There's a curious quasi-symmetry emerging. Is this the limit? By the way, this is all C+ as Popeye can be queried: ~1? 42 solutions ~1 halfduplex? 0 solutions h~1 halfduplex? 0 solutions.

after T.R.Dawson
(= 16+16 )

Duplex drawn position with 32 pieces
 
   
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(12) Posted by Joose Norri [Tuesday, Jan 11, 2022 12:37]

In Caissa's Wild Roses, Dawson gives two others by him in Chess Amateur 1923.


P1182095
(= 16+16 )

P1182096

(= 16+16 )



Dedicated with love to my wife
Construct legal positions with the usual 32 men on the 8 by 8 board, containing no retro-analytical argument, in which the mobility of the men is reduced to two moves.
 
   
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(13) Posted by Andrew Buchanan [Tuesday, Jan 11, 2022 13:36]

Thanks Joose,

Both of these tempt 1.b5xa6ep. I suppose that the e.p. convention (which would not count as retro-analytic argument?) would be used to scotch the cook. In the variant task that I proposed there is no such constraint, and I would want to eliminate the possibility by retro logic. This would imply dropping wK on a6 or a7. As a result, my initial forays with the first of the two positions you posted Joose don't take me beyond 38 white moves. The second one has moves for both players, so there is no dead position afoot.
 
   
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(14) Posted by Hauke Reddmann [Tuesday, Jan 11, 2022 18:25]

@Andrew: 42 is a nice number, I didn't want to
take that away from you :-)
BTW, I also remember (dimly) a position with 32 pieces
and only the wQ being mobile.
 
   
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(15) Posted by Joose Norri [Wednesday, Jan 12, 2022 00:54]

Hauke, that's P1106809
 
   
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(16) Posted by seetharaman kalyan [Wednesday, Jan 12, 2022 06:57]

The post was about double stalemate. Now we have moved to limited free moves.
 
   
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(17) Posted by Hauke Reddmann [Wednesday, Jan 12, 2022 09:50]

@seetharaman: That's called "thread drift" and is a very normal
phenomenon on social media. I can tell you some examples from
USENET where I started with the etymology of chess piece names
and it quickly went...uhm, are all readers 18+? :-)))
 
 
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MatPlus.Net Forum General Illegal Symmetric double stalemate with all pieces