15-puzzle Solvability

15-puzzle Solvability


15-puzzle is a quite old and famous puzzle, which had its own peak of interest!

In this mission you are given a position of tiles - a list of 4 lists of equal length with all integers from 1 to 16 incl. in arbitrary order (but number 16 always stands for empty place!). Your function should return a boolean value, if this combination of tiles is solvable (may be transformed by valid moves to "normal" order) or not, as True or False respectively.

Here is an interesting video about the puzzle itself and its solvability problem with the algorithm of checking explained. So if you don't like spoilers, you may try to solve the mission first without watching the video.

Input: A position of tiles as a list of 4 lists of integers from 1 to 16 incl.

Output: Solvability of puzzle as boolean value.


assert (
    fifteen_puzzle([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]])
    == True
assert (
    fifteen_puzzle([[15, 14, 13, 12], [11, 10, 9, 8], [7, 6, 5, 4], [3, 2, 1, 16]])
    == False
assert (
    fifteen_puzzle([[1, 5, 9, 13], [2, 6, 10, 14], [3, 7, 11, 15], [4, 8, 12, 16]])
    == True
assert (
    fifteen_puzzle([[1, 3, 2, 4], [5, 7, 6, 8], [9, 11, 10, 12], [13, 15, 14, 16]])
    == True

How it’s used: it's always interesting, what inner logic stands behind well-known games and puzzles.


  • len(position) == len(position[i]) == 4;
  • set(sum(position, [])) == {1, 2, ... 16}.

Invalid hot key. Each hot key should be unique and valid
Hot keys:
CheckiO Extensions

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In order to install CheckiO client you'll need installed Python (version at least 3.8)

Install CheckiO Client first:

pip3 install checkio_client

Configure your tool

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checkio serv -d

Alternatevly, you can install Chrome extension or FF addon

checkio install-plugin
checkio install-plugin --ff
checkio install-plugin --chromium

Read more here about other functionality that the checkio client provides. Feel free to submit an issue in case of any difficulties.

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