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
(In reply to tiny simplification thought
The 2x3 case seems harder to solve than the 3x3. Playing around, I can't seem to swap just one pair. But also, I don't see any parity constraint that would prevent a given permutation, such as a single pair swap.
Posted by Charlie
on 2004-11-08 17:47:02