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?

A little playing around convinced me I wasn't going to be able to do this without help.  Google found me a program:

http://www.ic-net.or.jp/home/takaken/e/15pz/index.html

It confirms the second has no solution and offers the following 51 move solution to the first:

  9  7  3  2  1 15 10  5  2  1
  6  9  7  3  8  2  1  6  9 14
 15  9  6  8  3  7 13 12 11 15
 14 13  8  6 13 11 12  8  7  3
  2  1  5 13  9 10 13  9 10 14
 15

The number indicates which number is moved to the blank space on each move.

Posted by Jer on 2013-02-15 11:42:51