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
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 90deg rotationally symmetric results (omitting results with only 180deg symmetry).
A more difficult problem might be finding all 37 nontrival 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 20160330 08:18:22 