Depicted below is one way to divide a 6x6 square into a four areas along the grid lines such that the division has 90 degree rotational symmetry.
+--+--+--+--+--+--+
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+ +--+--+ + +--+
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+ + + + + + +
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+ +--+--+--+--+ +
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+ + + + + + +
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+--+ + +--+--+ +
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+--+--+--+--+--+--+
How many ways are there to quarter a square like this?
(In reply to
re: computer solution by Charlie)
Looking up 1,5,51,1191 finds no sequence in Sloane's OEIS, but 1,3,26,596 does find A064941 Quartering a 2n x 2n chessboard (reference A003213) considering only the 90-deg rotationally symmetric results (omitting results with only 180-deg symmetry).
A more difficult problem might be finding all 37 non-trival variants of dividing the 6x6 board that don't necessarily have 90° rotational symmetry adding 11 to the 26 that do have such symmetry. (based on the referenced A003213).
Edited on March 30, 2016, 8:29 am
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Posted by Charlie
on 2016-03-30 08:18:22 |
re(2): computer solution
