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Quartering a Square (Posted on 2016-03-29) Difficulty: 3 of 5
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.
+--+--+--+--+--+--+
|  |              |
+  +--+--+  +  +--+
|        |     |  |
+  +  +  +  +  +  +
|        |     |  |
+  +--+--+--+--+  +
|  |     |        |
+  +  +  +  +  +  +
|  |     |        |
+--+  +  +--+--+  +
|              |  |
+--+--+--+--+--+--+
How many ways are there to quarter a square like this?

No Solution Yet Submitted by Brian Smith    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): computer solution Comment 4 of 4 |
(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
  Posted by Charlie on 2016-03-30 08:18:22

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