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3. Everything / Maths, Science & Technology / Mathematics

Solving the 15-number Puzzle

Most of us are familiar with the children's puzzle consisting of 16 squares with 15 numbered tiles that can be moved around the face of the puzzle.

When solved, the puzzle looks like this:

1234
5678
9101112
131415 

At the start it could look something like this:

134811
15914
23 6
7101215

Most people will try to solve this puzzle by quickly moving the number 1 tile up to the first position. This is why most people are unable to solve this puzzle quickly, because this approach is very difficult. The fastest solution is to make a snake of the numbers in order and drag the entire snake around the puzzle, adding new numbers on the tail until you have eight numbers in order. Notice that the first three numbers (1, 2 and 3) are already in a snake. Below is an example of a puzzle with the first eight numbers stretched out in a snake. It starts in the upper-right corner and ends in the upper-left corner.

811141
7 102
6543
1291315

Simply steer the snake around until you have filled the first two rows. You should get something like this:

1234
5678
 11910
12151314

You should be able to solve the puzzle now without disturbing the first eight tiles. Work only in the last eight tiles by making a snake of the next four numbers 9, 10, 11 and 12. It should be simple to construct this snake and steer it into place. If you are lucky, the last row will magically align as 15, 14, 13 and you will be able to steer this reverse snake into position to complete the puzzle. If you are unlucky, the last three numbers will have to be manipulated again. This will require that you temporarily break the continuity of the third row. Don't worry, it is easily restored. With this method you should be able to solve the puzzle within two minutes and very rarely over six minutes. Times over two minutes can be attributed to problems with the last row as it is counter-intuitive to the rest of the snake solution.

Looking at the completed puzzle you can see that the entire last 8 number snake should be in the order 9, 10, 11, 12, space, 15, 14 and 13.

1234
5678
9101112
131415 

Amaze your bar buddies with your new skill! Most palm pilots have this game on board. Nothing is more satisfying than waiting in a long grocery store queue and solving the problem on your palm pilot instead of reading the headlines on the trashy weeklies.


Discuss this Entry  People have been talking about this Guide Entry. Here are the most recent Conversations:

A nicer and faster way..
(Last Posting: May 14, 2003)

I've never done one of these in my life
(Last Posting: Mar 26, 2003)

5x4
(Last Posting: May 10, 2003)




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Entry Data
Entry ID: A1002826 (Edited)

Written and Researched by:
raymondo

Edited by:
U284


Date: 26   March   2003


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