How to Solve the 15 Puzzle

Introduction: How to Solve the 15 Puzzle

These instructions provide one method for solving the 15 Puzzle. The instructions provided here are meant to be a step by step process outlining one algorithm for solving the 15 Puzzle. These instructions are not meant to be an exhaustive explanation of how to move the tiles around the 15 Puzzle board. If the reader would like to learn more about the mechanics of the 15 Puzzle game, they are encouraged to experiment with the puzzle to learn how the tiles move around. My purpose here is to give instruction on where to put the pieces after you know how to move them around the board.

The 15 Puzzle is a good form of entertainment that has been popular for over 100 years. The puzzle is simple enough that it can be solved by children, but adults can have a difficult time solving it at first if they aren't good at solving puzzles. This set of instructions will be easy, and will only take 1 - 2 minutes for someone who is familiar with how to move the pieces around on a 15 Puzzle board. For beginners, solving the puzzle with these instructions can take 10 minutes or longer. This puzzle is fun, simple, and entertaining. Once you have solved the puzzle you will gain a sense of accomplishment. The skills you gain will help you to be able to solve more difficult puzzles. 

The 15 Puzzle is traditionally made up of the board shown in the picture above. However, sometimes a picture of a bird, a flower, or something else is swapped for the numbers, so instead of putting the numbers in order you try to put the image back together. In this version the numbers start out scrambled, and the goal is to slide the pieces around until you get them in order from 1 to 15 as shown in the picture above. 

All of the pictures in this set of instructions are screenshots of me playing the 15 Puzzle on my computer. The version of the puzzle shown in the pictures comes with Windows 7 in the Desktop Gadgets.

Solving this puzzle is not hazardous in any way that I know of. 

Step 1: Move the 1 Tile and the 2 Tile Into Their Final Positions

-Locate tiles 1 and 2.
-Move the tiles so that the blank space is in the next position you want to move the tile to.
-Move the tile into the blank space.
-Repeat this process until tiles 1 and 2 are in the correct positions.

Step 2: Move Tiles 3 and 4 Into Setup Positions

-Move tile 4 into tile 3's final position.
-Move tile 3 to be directly under tile 4.

Step 3: Move Tiles 3 and 4 Into Final Position

-Move the blank square to the top right corner.
-Move tiles three and four like they are a snake so that they are both in their final positions.

Step 4: Move Tiles 5 and 6 Into Final Position

-Locate tiles 5 and 6.
-Move tiles 5 and 6 to their final positions in a similar way that you moved tiles 1 and 2 into their final positions.

Step 5: Move Tiles 7 and 8 Into Setup Positions

-Move tile 8 into the final position of tile 7.
-Move tile 7 to be directly under tile 8.

Step 6: Move Tiles 7 and 8 Into Final Positions

-Move the blank space to be on the right hand side of tile 8.
-Move tiles 8 and 7 like a snake into their final positions.

Step 7: Move Tiles 13 and 9 Into Setup Positions

-Move tile 13 to be in tile 9's final position.
-Move tile 9 to be directly to the right of tile 13.

Step 8: Move Tiles 13 and 9 Into Final Positions

-Rotate the 5 tiles in the bottom left of the board counter clockwise like a snake until tiles 13 and 9 are in their final positions.

Step 9: Move Tiles 14 and 10 Into Setup Positions

-Move tile 14 to the right of tile 9 so that it is in tile 10's final position.
-Move tile 10 to be directly to the right of tile 14.

Step 10: Move Tiles 14 and 10 Into Their Final Positions

-Rotate the three tiles in the middle two columns on the bottom two rows counter clockwise like a snake until tiles 14 and 10 are in their final positions.

Step 11: Completing the Puzzle

-Rotate tiles 11, 12, and 15 either clockwise or counter clockwise until they are all in the correct positions

Step 12:

Congratulations!! You have solved the 15 puzzle!  If you are playing a version on the computer it will usually fill in the 16th square when you win so you can see the whole thing completed. If you get to the end and things aren't working, look back and double check all the numbers to make sure that they are all in the correct place. If you accidentally put a number in the wrong place on the top two rows it will be impossible to get the numbers into the correct spot at the end.

2 People Made This Project!


  • Furniture Contest

    Furniture Contest
  • Arduino Contest

    Arduino Contest
  • Explore Science Challenge

    Explore Science Challenge


Richard T Walker
Richard T Walker

Question 6 months ago

is it possible to to start with all the even from 2-14 and then all the odd numbers from 1-15. I have tried but I get 11.15,13 on the last row.
Richard T Walker


Answer 26 days ago

A click on a green square moves it to the neighboring empty cell. Use such clicks to order 15 numbers in the increasing order: 1 2 3 4 (first row), 5 6 7 8 (second row), 9, 10, 11, 12 (third row), 13, 14, 15, empty (fourth row).


3 years ago on Introduction

How do ik which ones are which cause the steps don't show the meloetta tiles?


4 years ago

Thank you! You saved my sanity.


Reply 3 years ago

Absolutely for me too. I wasn't able to do it by myself and I accepted it x3


4 years ago

A few tips:

- when solving for the end of a row (3 and 4, 7 and 8- i'll use 3 and 4 for this example), if it is more convenient to group the 3 tile with tiles 1 and 2 and solve for all three at the same time, you can position the 4 tile either under the 3 or under the spot where 4 should go. From here, you can slide 1 down, slide 2 and 3 to the left, and slide 4 up next to the 3, then slide everything back into place. The row should be completed.

--This can be done on any row above the last two for any position, however it is most viable to use for 3 and 4 in the 15 puzzle.

--This method is used much more frequently for puzzles bigger than 4x4.

- when solving for the last two rows, it is almost a necessity to solve for 9 and 13 first, but after that, a differing method can be used to finish the puzzle. Instead of solving for 10 and 14 next, one can instead solve for 10 and 11, then use a similar method to the one used in the first tip I mentioned. This entails sliding both to the side (putting 10 next to 13, and 11 next to 9), allowing you to cycle (rotate, as seen in step 11 of this tutorial) the 12 tile into position next to the 11 tile. From there, the whole 3x2 arrangement can be cycled clockwise to the solved position.

--This process can also instead be done solving for 11 and 12 instead of 10 and 11, with the later steps reversed.

--With puzzles bigger than 4x4, only use this method when 3x2 tiles remain unsolved.

Overall, this puzzle is very fluid- there are many strategies that can be used to solve it. I recommend finding out what strategies work best for you. With practice, you can even beat the current Guinness world record (10 puzzles consecutively solved in 3 minutes 51 seconds). Good luck, reader.


5 years ago

I get to the end and the 12 and 11 are in the wrong place. How do I solve that?


Reply 5 years ago

Hello JoelH50. It has been a few years since I have played around with the 15 puzzle. However, I am not sure I ever encountered a case with the 11 and 12 being in the wrong places if all the other tiles were in the correct locations. Are you playing on a computer or on a physical 15 Puzzle game? If you are playing on a physical 15 puzzle game it is possible that someone took some of the tiles out and switched their places. If that is the case it is likely that your puzzle is impossible to solve. The tiles in the game aren't allowed to be scrambled randomly to any position, so if some of the tiles have been physically removed and swapped locations the puzzle may be impossible to solve. You can find more info on 15 Puzzles on various websites including Wikipedia.

Hope this helps.


Reply 4 years ago

This is just an earlier end to a puzzle when 14 and 15 will be the wrong way round -= you can swap 11 and 12 round but then 14 and 15 will be wrong