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Balancer's Chess

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A chessboard is balanced on a tack at the center.

post-53237-0-15575000-1365191029_thumb.j

How would you place the pieces on any center
of the 1x1 squares to keep the board in balance
if the weights are :Pawn=1 Knight=3 Bishop=3
Rook =5 Queen=9 King=11

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9 answers to this question

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Posted (edited) · Report post

Standard chess setup, except one side K-Q reversed, e.g.



R N B Q K B N R
P P P P P P P P
---------------------
--------------------
--------------------
--------------------
P P P P P P P P
R N B K Q B N R
Edited by jhawk
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Posted · Report post

Standard chess setup, except one side K-Q reversed, e.g.

R N B Q K B N R

P P P P P P P P

---------------------

--------------------

--------------------

--------------------

P P P P P P P P

R N B K Q B N R

1 of each kind K,Q,R,B,N,P - 6 pieces only

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Posted · Report post

--------
-N------
--K-----
---P----
----R---
-----Q--
------B-
--------

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Posted · Report post

--------
-N------
--K-----
---P----
----R---
-----Q--
------B-
--------

It will tilt

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Posted · Report post

Whoops, I see my error.

B-------
--------
--K-----
--------
----R---
-----Q--
------N-
-------P
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Posted · Report post

Whoops, I see my error.

B-------
--------
--K-----
--------
----R---
-----Q--
------N-
-------P

I got 9 solutions so far and yours make it 10. Thanks

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Posted · Report post

What if there were no diagonals?

. - - - - - - .

- . - - R - . -

N - . - - . B P

- - - . . Q - -

- - - . . - - -

- - . - - . - -

- . K - - - . -

. - - - - - - .

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Posted · Report post

What if there were no diagonals?

. - - - - - - .

- . - - R - . -

N - . - - . B P

- - - . . Q - -

- - - . . - - -

- - . - - . - -

- . K - - - . -

. - - - - - - .

x-axis moment

(3)(3.5)+11(1.5)=(5)(0.5)+(9)(1.5)+(3)(2.5)+(1)(3.5)

y-axis moment

(11)(2.5)=(9)(.5)+(3+3+1)(1.5)+(5)(2.5)

Nicely balanced structure..

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Posted · Report post

What if there were no diagonals?

. - - - - - - .

- . - - R - . -

N - . - - . B P

- - - . . Q - -

- - - . . - - -

- - . - - . - -

- . K - - - . -

. - - - - - - .

x-axis moment

(3)(3.5)+11(1.5)=(5)(0.5)+(9)(1.5)+(3)(2.5)+(1)(3.5)

y-axis moment

(11)(2.5)=(9)(.5)+(3+3+1)(1.5)+(5)(2.5)

Nicely balanced structure..

Actually it's just two diagonal solutions. Apply one to x and the other to y.

I just had to adjust one of them, to get a piece in each quadrant.

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