Problem 42842. The sliding puzzle: 15

Created by HH

Solve Later

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If you are unfamiliar with the sliding puzzle, enter the command fifteen in your MATLAB command window (or search online, of course). In this problem you are tasked with solving the puzzle.Given a scrambled classic 4-by-4 sliding puzzle, return a set of moves that solves it.The puzzle is represented by a size [4 4] array, p, with integers from 1 to 15 representing the different tiles, and 0 representing the open slot. A single move is represented by an integer that is the linear index of the the tile you wish to slide into an adjacent open slot. A solution is represented by a row vector, m, of moves, the application of which results in a correctly arranged puzzle.The solution does not have to be efficient. It must simply result in a correctly solved puzzle. Illegal moves, such as trying to slide a tile that is not adjacent to the open slot, will be ignored.Example: (the leading zeros are added only for easier visualization)<pre> p = [ 01 02 03 04;</pre><pre> 05 10 06 07;</pre><pre> 09 00 11 08;</pre><pre> 13 14 15 12]</pre><pre> m = [6 10 14 15 16]</pre>

If you are unfamiliar with the sliding puzzle, enter the command _fifteen_ in your MATLAB command window (or search online, of course). In this problem you are tasked with solving the puzzle.

Given a scrambled classic 4-by-4 sliding puzzle, return a set of moves that solves it.

The puzzle is represented by a size [4 4] array, p, with integers from 1 to 15 representing the different tiles, and 0 representing the open slot. A single move is represented by an integer that is the linear index of the the tile you wish to slide into an adjacent open slot. A solution is represented by a row vector, m, of moves, the application of which results in a correctly arranged puzzle.

The solution does not have to be efficient. It must simply result in a correctly solved puzzle. Illegal moves, such as trying to slide a tile that is not adjacent to the open slot, will be ignored.

Example: (the leading zeros are added only for easier visualization)

p = [ 01 02 03 04;

05 10 06 07;

09 00 11 08;

13 14 15 12]

m = [6 10 14 15 16]

Solve

Solution Stats

127 Solutions
20 Solvers

Last Solution submitted on May 12, 2021

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

Are Mjaavatten on 14 Jul 2018

The most challenging cody problem I have tried so far. Had to teach myself some stuff that I knew little about before, That is a quality indicator!

HH on 15 Jul 2018

Thanks, Are. Now try problem 44376. https://www.mathworks.com/matlabcentral/cody/problems/44376

Sophia Nguyen on 21 Feb 2020

I have tried repeatedly. The code works well and only took 2s max in my computer, but the system keeps outputting error caused by long running matlab code.

Solution Comments

Solution 3052225

2 Comments

2 Comments

Johanna Richter on 4 Oct 2020

oh my god finally :D this one drove me crazy
code is not nice, because i had some really dumb mistakes in the process, but i'm too lazy to write it all again
really challenged me hardcore!

Johanna Richter on 4 Oct 2020

I would really love to apply the answer i found to the GUI opening when i call "fifteen"... I would also have to read the situation to start with from there.
Can anyone help me on how to do this to visualize the moves?

Problem Recent Solvers20

Problem Tags

15 fifteen puzzle sliding

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