bonanova Posted March 2, 2009 Report Share Posted March 2, 2009 I have a chess board that has 13 squares on a side. I want to break it [along the borders of the individual squares] into smaller square pieces. I could make a 12x12 square and 25 1x1 squares - 26 in all. I could make a 7x7 square, 3 6x6 squares and 12 1x1 squares - 16 in all. What is the fewest I could make? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 One 13x13 square. "Want" doesn't equal "have to". Okay, lame answer. I have to go to work. Will work on this there. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 I can do it with 13. One 8x8, two 5x5, three 3x3, and 7 2x2. I don't know if this is the ultimate answer, but I suspect the final solution would have zero 1x1 squares. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 12 8x8, 3- 5x5's, 2 - 3x3's, 2- 2x2's, 4- 1x1's Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 12 8x8, 3- 5x5's, 2 - 3x3's, 2- 2x2's, 4- 1x1's 12 is the smallest number, although I did it with 1 7x7, 2 6x6, 1 5x5, 5 2x2 and 3 1x1 squares. I've quickly come to learn that the next question will be: what is the optimal solution for a board of dimensions nxn, where n is odd. (n+11)/2, for n > 3. The division consists of 1 ((n+1)/2)x((n+1)/2) square, 2 ((n-1)/2)x((n-1)/2) squares, 1 ((n-3)/2)x((n-3)/2) square, (n-3)/2 2x2 squares, and 3 1x1 squares. Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted March 2, 2009 Report Share Posted March 2, 2009 Eleven. 1 - 7x7 2 - 6x6 1 - 4x4 1 - 3x3 3 - 2x2 2 - 1x1 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 I only count 160 sq. units of area there, rather than 169. Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted March 2, 2009 Report Share Posted March 2, 2009 Eleven. 1 - 7x7 2 - 6x6 1 - 4x4 2 - 3x3 3 - 2x2 2 - 1x1 I only count 160 sq. units of area there, rather than 169. Your right, I didn't list them all. Same answer though. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 I got twelve. 2- 7x7s, 4-2x2, 2-4x4s and 4-3x3s Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 2, 2009 Author Report Share Posted March 2, 2009 I got twelve. 2- 7x7s, 4-2x2, 2-4x4s and 4-3x3s Since any 7x7 division includes the center square, you can have only one of them. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 3, 2009 Report Share Posted March 3, 2009 WELL... If you cut it 0 times you get 1 square thats 13 x 13, but something tells me thats not the answer you were looking for... Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 3, 2009 Author Report Share Posted March 3, 2009 WELL... If you cut it 0 times you get 1 square thats 13 x 13, but something tells me thats not the answer you were looking for... Pieces is plural. Quote Link to comment Share on other sites More sharing options...
Question
bonanova
I have a chess board that has 13 squares on a side.
I want to break it [along the borders of the individual squares] into smaller square pieces.
I could make a 12x12 square and 25 1x1 squares - 26 in all.
I could make a 7x7 square, 3 6x6 squares and 12 1x1 squares - 16 in all.
What is the fewest I could make?
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