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Permuting a Square (Posted on 2004-11-08) Difficulty: 4 of 5
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

See The Solution Submitted by Brian Smith    
Rating: 4.2857 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: tiny simplification thought | Comment 4 of 9 |
(In reply to tiny simplification thought by nikki)

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

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