Given a 3x3 square with 9 distinct entries, can all permutations of the elememts in the square be reached when the only legal operation is to rotate a 2x2 subsquare 90 deg clockwise? (A rotation on the same subsquare may be done multiple times.) If not how many positions are attainable?

Example, rotating the upper left 2x2 square.
1 2 3    4 1 3
4 5 6 -> 5 2 6
7 8 9    7 8 9

Hmmm, I wonder if I can do the following… can I show, for a 2x3 rectangle, that I can rotate things around and get every permutation? If so, then I can see if I can show each way to get the various permutations of the top row, and then it will follow that all other permutations can be found (based on the 2x3 rectangle proof).

I have no idea how to prove that though.

Programmers, away! =)

Posted by nikki on 2004-11-08 14:23:11