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?

(In reply to computer solution by Charlie)

Scaled up to 8x8 there are 1191 such patterns, or 1190/2+1 = 596, if reflections are eliminated.  I only had to fix one bug in the program where I had hard coded a 3 instead of sz/2.

Posted by Charlie on 2016-03-29 16:08:03