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 A square question (Posted on 2010-10-12)
1. Given a 7*9 grid with distinguishable (e.g. numbered) tokens on each square.
2. Move each one of the tokens to a neighboring place (horizontally, vertically-but not diagonally).
3. Evaluate the number of possible distinct solutions.

Remember: each token has to arrive to a square occupied initially by its neighbor.

4. Please submit the final answer and the amount of time spent to get it.

 No Solution Yet Submitted by Ady TZIDON Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Fast solution (spoiler) | Comment 1 of 2
Color squares alternating black and white, like a chessboard.  Then each token originally on a black square must finish on a white square, and vice versa.  But the matrix has an odd number of squares, so the number of black and white squares is unequal.  Therefore, there is no way to accomplish the rearrangement.

Total number of distinct solutions: 0
Total time to solve: less than a minute (it took longer to write it down).

 Posted by Steve Herman on 2010-10-12 23:42:37
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