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 CHESS SOLVINGTournamentsRating lists1-Apr-2023
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Please don't cheat by going to CSE (or writing a program like CSE did).
I'm looking at you, Rewan :-)

Place all 16 (standard) men of White, the black king and some black pawns
on the chessboard. No piece shall be attacked or defended.
Maximize "some". (If this has been done before, which wouldn't surprise

I'll leave this one up to the mastes. :-)

Pawns also should be undefended?

Yes, of course, or I had said "officers".
(This ambiguity of "piece" is a bit annoying;
I don't ever have the problem in German :-)

3 BP, but not feels as maximum

I have 4 black pawns.

@Ulrich: So does CSE. A proof that 7 pawns can't be surpassed
is obvious by a square counting argument which isn't even that refined,
so methinks this could be a strictly provable optimum.

If you require legal positions, there is a very simple proof that the maximum is 5 black pawns.

Here is a construction with 4 black pawns:

(= 16+5 )

Maybe someone can improve on that...

@Ulrich: Shoot. (The proof. :-) The CSE solution differs
vastly from yours (it surprises you got away with
QBB not all on the border - Qb8 Bg1 Bh1 or so should
be better a priori, because of less squares lost
diagonally).

Are you sure about that? Losing squares on a Bishop or Queen diagonal is a problem only if those squares are not covered by rooks already. Or rather, try to maximize the number of squares that remain available after Queen, Rooks and Bishops:

Qd1, Rb4, Rf2, Ba8, Bg5 (my solution): 18

Qb8, Rc3, Rf5, Bg1, Bh1 (for example): 17

Here is another puzzle that might serve as a basis for solving yours: After placing QRRBB, what is the maximum number of squares that can remain available?

Is there any virtue in maximizing Black force? E.g. in Ulrich’s example bPa3 might be replacing by bS

@Andrew: Think that's not so relevant since maximizing count
(not force) was the idea. One could make a different puzzle out of this:

Legal position, maximum material (Q=8,R=5,BS=3,P=1),
no protections or captures. I doubt if 6Q+KK can
be beat then.

Well I know it's a variant idea. That's why I suggested it. Can't invalidate it just because it's different from your previous concept. Now, I was only suggesting it for the Black force. However your variant's variant of maxing over all force is interesting too. Obviously one can do better than 2K+6Q:

(= 7+2 )
An interesting question is whether a configuration exists for one of the 12 essential solutions to the eight queens problem, under which a *second* vacant square is released by the change of 2 queens to kings. This doesn’t seem to lead to a solution, but possibly there is one where the kings and pawns form a square.

Full white force + 5 Black pawns would be 39+5=44. This new solution would be 54+3=57.

See how fruitful it is to welcome variants, Hauke? :) Happy season's greetings :) :)

@Andrew: You know the term "reverse psychology"? I was just too lazy
to find a position where 6Q yield 3 unprotected squares, and you
promptly delivered :P Of course I like variants (e.g. the just published
SCHWALBE construction challenge item B is a close variant to one
we did together here on 16-Oct-09), so Merry Xmas to you too!

(15) Posted by Andrew Buchanan [Saturday, Dec 24, 2022 10:47]

I’m too lazy to do reverse psychology :-) Chess is easier