Brian-E:

Your third criticism (that I can't count!) was completely valid...it's called proof by fatigue! :-). Have a look at the fixed-up and expanded version; lets get all the chess notations right, because not everyone can ignore my minor errors as easily as you...

I went ahead and completed the calculation for the number of legal positions with three men on the board, except for the numbers....

[QUOTE=Christenson;258848]Brian-E:

Your third criticism (that I can't count!) was completely valid...it's called proof by fatigue! :-). Have a look at the fixed-up and expanded version; lets get all the chess notations right, because not everyone can ignore my minor errors as easily as you...

I went ahead and completed the calculation for the number of legal positions with three men on the board, except for the numbers....[/QUOTE]
I'll PM you with the small number of trivial notation errors I found.
Regarding the very interesting last section of your document (which I have so far only sweepingly perused), I would like to suggest that in addition to the configurations with king and bishop versus king which are illegal, there may be some involving king and rook versus king too. Knight and queen do seem to be completely free in their placements though.
For example with the rook, is the configuration below legal?

Oh Brother! No....black K cannot have just moved into check; white rook cannot have just moved through white K to put it in check....(also means we've got *MORE* problems with bishops -- e.g. WhiteK on a6, black bishop on c8, black K on c7. I'm not so sure on Queens and knights). Unfortuneately, this will have to wait a bit as I have to go get work on a paycheck today....

[QUOTE=Christenson;258874]Oh Brother! No....black K cannot have just moved into check; white rook cannot have just moved through white K to put it in check....
[/QUOTE]

The [I]configuration[/I] is perfectly legal. The [I]position[/I] is legal with black to move only. The previous move would have been bxa8=R+. And slapping black silly for not moving away whatever was on a8 [I]should[/I] be legal, but is probably not, in most parts of the world.

Note that the of the 16 mirrored configurations "identical" to this one, only 4 represent legal positions.

[QUOTE=Christenson;258874](also means we've got *MORE* problems with bishops -- e.g. WhiteK on a6, black bishop on c8, black K on c7. I'm not so sure on Queens and knights). Unfortuneately, this will have to wait a bit as I have to go get work on a paycheck today....[/QUOTE]

That configuration doesn't even require (or allow, for that matter) minor promotion to make the position legal with white to move[*]. Black just played Bx[QR]c8+, drawing.

Add any black piece on d7 for an illegal configuration with legal mirrors. :smile:
[*] [B]Edit:[/B] For reasons of clarity: White is not actually "to move". The game ended after black's last move.

[QUOTE=Brian-E;258865]I'll PM you with the small number of trivial notation errors I found.
Regarding the very interesting last section of your document (which I have so far only sweepingly perused), I would like to suggest that in addition to the configurations with king and bishop versus king which are illegal, there may be some involving king and rook versus king too. Knight and queen do seem to be completely free in their placements though.
For example with the rook, is the configuration below legal?[/QUOTE]Promotion of pawn to rook?

Paul

[QUOTE=Brian-E;258865]I'll PM you with the small number of trivial notation errors I found.
Regarding the very interesting last section of your document (which I have so far only sweepingly perused), I would like to suggest that in addition to the configurations with king and bishop versus king which are illegal, there may be some involving king and rook versus king too. Knight and queen do seem to be completely free in their placements though.
For example with the rook, is the configuration below legal?[/QUOTE]

I could see a way assuming it's a8 and b8 that the white pieces are on.

black king is one step behind( off to the far side) of the white pawn it is in capture mode it captures a black pawn on a7 the white king moves ahead the pawn moves ahead and promotes to a rook.

Yep, I was just testing you all.:rolleyes:

Well, no, not really, after forgetting earlier that pawns capture diagonally and looking silly afterwards, this time I've forgotten about pawn promotions to rooks now. Why did I have to put the board [I]that[/I] way round?

Still, as ckdo points out, some of the rotations or reflections of the configuration are illegal.

Some of those K+B vs K positions in Eric Christenson's document which he discounts as illegal will have to be counted back into the total too if the bishop may have just promoted from a pawn.

Can anyone find any K+Q vs K or K+N vs K configurations which are illegal (apart from putting the kings next to each other of course)? I'd like to stick my neck out and say that after placing the two kings legally, a queen or knight can always legally go on any remaining square, but am I correct?

[QUOTE=Brian-E;258968]
Can anyone find any K+Q vs K or K+N vs K configurations which are illegal (apart from putting the kings next to each other of course)? I'd like to stick my neck out and say that after placing the two kings legally, a queen or knight can always legally go on any remaining square, but am I correct?[/QUOTE]

at last check all knight and 2 king positions are possible but last I checked they'd all get drawn for insufficient materials. the queen ones as far as I can tell would be all legal as with the rooks the bishop ones get caught on the fact that if the kings block part of a diagonal not all possible combos of places are legal.

It's clear I'm confused when in a hurry to work in the morning. The second king was on the wrong place, as noted! :-( And the trivial notational problems were, indeed, problems, Brian. Thanks.

I have, for K-R-K:
WhiteK on b8, black K on a6, WhiteR on a8 as legal, since the pawn *could* have captured into that position and been promoted.
However, if I reverse colors, the position is illegal, since the rook can't have been just promoted.
Likewise, if I have whiteK on a7, white R on a8, and black K on c8, the position is not legal since if the rook was just promoted, the black K was in check on the previous move.
Swap colors, also illegal, no way to get the R to the right place.
If the King were further away, the other king could have moved out of the way for a discovered check.

Multiply these cases by 4 corners of the board, to get 12 K-R-K positions illegal out of the 3612*2*62.

Now, for K-B-K, i have, basically, if the friendly K blocks access to the edge square the bishop is on, and the opposing king is attacked, and the bishop can't be a freshly promoted pawn, the position is illegal. That is, for examples:
a) White K on g8, White B on h7, and Black K on any of g6,f5,e4,d3,c2,b1, the position is illegal. (latest version of document, above, catches the g6 case, misses the others)
b) If the white B is on a1, and the black K on b2, and the white K anywhere else, the position is illegal.

I don't think there are others. Time I did garbage duty, and be home late tomorrow after finding out why Windows crashed some of my primecrunchers last night.

The dinosaurs knew about chess and what it really means.

[url]http://www.qwantz.com/index.php?comic=1942[/url]

[QUOTE=diep;258176]As for the estimate: there is 2 requirements for 1 side to be able to castle.
A king must be on e1 (resp e8) AND the original rook must be on a1.[/QUOTE]

There are several requirements for the king to be able to castle and you've only shown one of them. They are:
1. As you stated, both must be in their original position.
2. Neither king nor rook can have previously moved during the game. Even if they are in their original position, if they have moved and then moved back to their original square, then castling is not allowed.
3. You cannot castle OUT of check.
4. You cannot castle INTO check.
5. You cannot castle OVER check.

As examples for #3, 4, & 5: For the white queenside castle where the king is on e1 and rook is on a1, if the squares c1, d1, or e1 are being directly attacked by the opposing side, you cannot castle; an attack on e1 because of reason 3, d1 because of reason 5, and c1 because of reason 4.

One question : When determining "different" chess positions, is it considered a different position if it is white to move than if it is black to move even if all of the pieces are in the same place? I would think so because it makes a big difference in whether it is a legal position. If it is white to move, than white can legally be in check -or- even in checkmate. Obviously it would be illegal if it was black to move in the same position.


Gary