Configuration - 1               Configuration - 2

+----+----+----+----+        +----+----+----+----+
| 8  | 7  | 9  | 4  |        | 8  | 7  |  9 | 4  |
+----+----+----+----+        +----+----+----+----+
| 5  | 3  |    | 13 |        | 5  | 3  |    | 13 |
+----+----+----+----+        +----+----+----+----+
| 10 | 2  | 6  | 12 |        | 10 | 2  | 12 | 6  |
+----+----+----+----+        +----+----+----+----+
| 15 | 1  | 14 | 11 |        | 15 | 1  | 14 | 11 |
+----+----+----+----+        +----+----+----+----+

The task is to place the tiles in order to complete the 15 Puzzle.

Which of the above configurations does not have a solution and why?

For the configuration having a solution, what is the minimum number of moves to achieve this?

As the link notes if the blank is in the bottom right corner you can find the parity of the permutations required to bring the puzzle to its solved position.  If this number is odd the puzzle is unsolvable.

So I slid the 13 over and the other two up to get the blank into the bottom corner, then I counted permutations.

I'm not sure if these are the minimum number of permutations but I found a way to do the first puzzle with 16 swaps and the second with 17.

This would indicate the second puzzle has no solution.

Edited on February 15, 2013, 11:39 am

Posted by Jer on 2013-02-15 11:19:22