How to Solve a 15 Puzzle

In this article, you will learn how to solve a 15 puzzle. Once you memorize the rules, your solving record can be reduced to a few minutes.

Method 1
Method 1 of 3:

Solving the First Row

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    1
    Place 1 and 2 on their original places.
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    Place 4 on the right side of 2.
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    Place 3 under 4.
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    Make an empty space on the right side of 4.
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    Push 4 to the empty space.
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    Push 3 upward.
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Method 2
Method 2 of 3:

Solving the Second Row

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    Place 5 and 6 on their original places.
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    2
    Place 8 on the right side of 6.
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    Place 7 under 8.
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    4
    Make an empty space on the right side of 8.
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    Push 8 to the empty space.
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    Push 7 upward.
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Method 3
Method 3 of 3:

Solving the Third and Fourth Rows

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    Place 13 on the original place of 9.
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    Place 9 on the right side of 13.  Move 13 temporarily if you have to.
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    Make an empty space under 13.
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    Push 13 downward.
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    Push 9 leftward.
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    6
    Place 14 on the original place of 10.
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    Place 10 on the right side of 14.  Move 14 temporarily if you have to.
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    Make an empty space under14.
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    Push 14 downward.
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    Push 10 leftward.
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    11
    Move around the blocks 11, 12, and 15 to put them to their original places.  If they don't go to their original places, do method 3 again by mixing only the last two rows.
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Community Q&A

  • Question
    I can solve 1 through 12, but when I go on to the last row, 13 is at the end, and 14 and 15 are at the front. What am I doing wrong?
    Stephen Han
    Stephen Han
    Community Answer
    In that case, you have to do part three all over again. If you follow the steps, 13 has to be at the bottom of 9, and 14 has to be at the bottom of 10.
  • Question
    How do I change only two tiles?
    Community Answer
    Community Answer
    A single swap is known to be impossible. In this type of puzzle, exactly half of the positions are obtainable, those that require an EVEN number of swaps from the starting position.
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About This Article

wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, volunteer authors worked to edit and improve it over time. This article has been viewed 46,227 times.
53 votes - 66%
Co-authors: 8
Updated: December 23, 2021
Views: 46,227
Categories: Mathematical Puzzles
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