TimeSpaceLightForce Posted April 5, 2013 Report Share Posted April 5, 2013 A chessboard is balanced on a tack at the center. 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 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted April 7, 2013 Report Share Posted April 7, 2013 What if there were no diagonals? . - - - - - - . - . - - R - . - N - . - - . B P - - - . . Q - - - - - . . - - - - - . - - . - - - . K - - - . - . - - - - - - . 1 Quote Link to comment Share on other sites More sharing options...
0 jhawk Posted April 5, 2013 Report Share Posted April 5, 2013 (edited) 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 April 5, 2013 by jhawk Quote Link to comment Share on other sites More sharing options...
0 TimeSpaceLightForce Posted April 6, 2013 Author Report Share Posted April 6, 2013 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 Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted April 6, 2013 Report Share Posted April 6, 2013 -------- -N------ --K----- ---P---- ----R--- -----Q-- ------B- -------- Quote Link to comment Share on other sites More sharing options...
0 TimeSpaceLightForce Posted April 7, 2013 Author Report Share Posted April 7, 2013 -------- -N------ --K----- ---P---- ----R--- -----Q-- ------B- -------- It will tilt Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted April 7, 2013 Report Share Posted April 7, 2013 Whoops, I see my error. B------- -------- --K----- -------- ----R--- -----Q-- ------N- -------P 1 Quote Link to comment Share on other sites More sharing options...
0 TimeSpaceLightForce Posted April 7, 2013 Author Report Share Posted April 7, 2013 Whoops, I see my error. B------- -------- --K----- -------- ----R--- -----Q-- ------N- -------P I got 9 solutions so far and yours make it 10. Thanks Quote Link to comment Share on other sites More sharing options...
0 TimeSpaceLightForce Posted April 8, 2013 Author Report Share Posted April 8, 2013 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.. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted April 9, 2013 Report Share Posted April 9, 2013 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. Quote Link to comment Share on other sites More sharing options...
Question
TimeSpaceLightForce
A chessboard is balanced on a tack at the center.
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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