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
Visually and doing mental manipulations, it seems to me that all permutations can be done using a 2x2 sub-square.
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Posted by Osi
on 2004-11-08 14:23:55 |
Thoughts
