superprismatic Posted October 16, 2009 Report Share Posted October 16, 2009 Consider a variant of the 8 Queens problem: you must place an equal number of knights and queens on a chessboard such that no piece attacks any other piece. What is the maximum number of pieces you can so place on the board, and how many different ways can you do it? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 16, 2009 Report Share Posted October 16, 2009 If anyone needs a chess board All I can come up with is 4 of each Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted October 17, 2009 Author Report Share Posted October 17, 2009 If anyone needs a chess board All I can come up with is 4 of each You can do better than 4 each! Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted October 17, 2009 Report Share Posted October 17, 2009 5 Queens and 5 Knights Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 17, 2009 Report Share Posted October 17, 2009 The prof if right I think. N Queens will take up N rows and N columns. If N was 6 this would leave only 2 rows and 2 columns (i.e 4 squares free) for the 6 knights. Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted October 17, 2009 Author Report Share Posted October 17, 2009 Prof. Templeton has a correct answer and psychic_mind has a good proof that 6 of each can't work. All that's left is to see how many ways you can place 5 queens and 5 knights on the board so that no piece attacks any other. Any takers for this? Quote Link to comment Share on other sites More sharing options...
Question
superprismatic
Consider a variant of the 8 Queens
problem: you must place an equal
number of knights and queens on a
chessboard such that no piece
attacks any other piece. What is
the maximum number of pieces you
can so place on the board, and how
many different ways can you do it?
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