Question 28577: Is the following 15 puzzle solvable or unsolvable?
2 1 3 4
5 8 7 6
9 10 12 11
15 13 14 *
Answer by astromathman(21)   (Show Source):
You can put this solution on YOUR website! It is not solvable. It takes 7 swaps of adjacent pairs to "solve" it. Since 7 is an odd number, it is not solvable. If it took an even number of swaps, it would be solvable.
Note:
In the first row, swap 2 and 1.
In the third row, swap 11 and 12.
In the 4th row, 15,13,14 --> 13, 15, 14 --> 13,14,15 (2 swaps)
In the second row, 5, 8, 7, 6 --> 5, 7, 8, 6 --> 5, 7, 6, 8 --> 5, 6, 7, 8 (3 swaps).
That's 7 swaps altogether.
To try it out, go to http://www.javaonthebrain.com/java/puzz15/. You can get everything down to a single pair out of order, but no further.
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