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There is an intellectual puzzle 3x3, as in the photo:

enter image description here

You need to get an ordered set by moving the buttons through an empty area, like:

enter image description here

Question: Is a 4x4, 5x5, 6x6 game possible?

Sub-question: Does this game have an official name?

Thanks in advance for any comment/answer!

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  • $\begingroup$ Should not this be in beta group, as this is not actually a puzzle. $\endgroup$ – Pandey_Ji Jun 20 '20 at 14:53
  • $\begingroup$ @Pandey_Ji Yes, you are probably right. $\endgroup$ – alexrnov Jun 21 '20 at 4:22
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    $\begingroup$ Why not add the tag puzzle-identification? This is essential to the original spirit of this site, as far back as question #80. $\endgroup$ – humn Jun 21 '20 at 14:49
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The game is usually referred to as a Sliding puzzle

The most famous example is the 15 Puzzle ($4 \times 4$ version)

In this example, half of all the possible starting positions are solvable. In particular, if we switch the 15 and 14, then the puzzle becomes unsolvable. (see Sam Loyd's unsolvable 15-puzzle).

Higher order examples
Although I have not seen physical example of $5 \times 5$ or $6 \times 6$, I have seen some online, see here for example: https://www.castleviewuk.com/stp_bk_6x6.html
Googling about might give you some better results.

If you like these types of puzzles you may also enjoy

Rush Hour
Klotski

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    $\begingroup$ On a side note, I think spoiler isn't necessary (?) $\endgroup$ – athin Jun 20 '20 at 8:35
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    $\begingroup$ @hexomino Thank You very much for the detailed answer and links! $\endgroup$ – alexrnov Jun 20 '20 at 8:38
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    $\begingroup$ @athin, yes, you're right, force of habit! I'll take them out. $\endgroup$ – hexomino Jun 20 '20 at 10:26
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Question: Is a 4x4, 5x5, 6x6 game possible?

Yes! This puzzle can be played with arbitrary size such as in Tatham's version. You can play it in your browser or download a Windows executable from the main page that is full of other puzzles too!

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    $\begingroup$ @DanielMathias: Why so? It answers the main question "Is a 4x4, 5x5, 6x6 game possible?". $\endgroup$ – user21820 Jun 20 '20 at 18:21
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    $\begingroup$ Agreed, the comment was automatically sent from review. I still think would be better as a comment, as hex has provided a full answer and this doesn’t contribute too much else apart from some useful links, but I agree it does answer the question $\endgroup$ – Beastly Gerbil Jun 20 '20 at 18:34
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    $\begingroup$ @DanielMathias: So what if an answer has been accepted? Since the beginning the SE guidelines have encouraged multiple helpful answers, and never once said that an accepted answer indicates that nobody else should answer. I posted my answer only because the currently accepted one links to an inferior version. $\endgroup$ – user21820 Jun 20 '20 at 18:37
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    $\begingroup$ @BeastlyGerbil: Thanks for responding! See my above comment for why I think my answer should not be just a comment. $\endgroup$ – user21820 Jun 20 '20 at 18:38
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    $\begingroup$ @user21820 Thank You for the answer and links! $\endgroup$ – alexrnov Jun 21 '20 at 0:06

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