I have a wooden snake puzzle in my collection that has been unsolved for years. I wondered if any of you might be interested. I have fiddled with it, but think it might need dynamic programming or something to solve. But maybe some of you have an approach that would work.

The puzzle is pictured below. It consists of 64 wooden cubes each of which (except the ends) has a hole in the center of two of the faces. An elastic is threaded through the whole thing so that the pieces can swivel in place. The objective is to arrange it into a 4x4x4 cube.

Snake Puzzle

So, for example, starting at the bottom end (in the picture), there are 3 in a row. The last of these three has the fourth cube coming off at right angles. The direction it comes off can be swivelled, and that entire next segment (also 3 in a row: blocks 4-6) can swivel around so that it doubles back on itself, or sticks out at right angle or continues straight with a kink.

The last of these is impossible, of course, because the length would be 5 and therefore it would not fit into a 4x4x4 cube.

Here is a description of the entire snake:

3 - 2 - 3 - 2 - 2 - 4 - 2 - 3 - 2 - 3 - 2 - 3 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 3 - 3 - 2 - 2 - 2 - 2 - 2 - 3 - 4 - 2 - 2 - 2 - 4 - 2 - 3 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 4 - 2

In the above sequence, each corner is counted twice. There are 46 segments, so 45 corners, which is why the above numbers sum to 109 rather than 64. Hopefully that makes sense.

Would love to hear your thoughts. Even partial insights would be helpful.


Thanks to @Jaap Scherphuis, it is now neatly solved! Me: >10 years without success. The internet: <1h. Gotta love it.

Snake puzzle - solved

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    $\begingroup$ I bought that a couple of months ago. Now here I am, on Puzzling; reading through this very post; looking at this very particular puzzle. Sometimes, I feel like I might have cosmic powers... (though I, as well, could not turn the wooden snake into a cube). $\endgroup$ – Mr Pie Jul 20 '18 at 5:52

I have the same snake cube puzzle, except that its cubes don't alternate in colour. On mine they are coloured so that the finished cube consists of 2x2x2 blocks.

Drawing of the solution is under the spoiler:

enter image description here

The 3x3x3 version of this puzzle is very common, though almost all versions use the same configuration of straight and bent cubes. You can find out more about these smaller versions on my snake cube page.

  • $\begingroup$ That's amazing! How did you solve it in the first place? Or did you somehow maintain the solution? $\endgroup$ – Dr Xorile Oct 19 '17 at 19:07
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    $\begingroup$ I solved mine by hand, but it is easier than yours because of the colouring. I also have a javascript program to solve the 3x3x3 version on the page I linked to. A few years ago I adapted that script to work for the 4x4x4 to create the picture above. If I remember correctly, the script also showed that the solution is unique (up to rotation/reflection). $\endgroup$ – Jaap Scherphuis Oct 19 '17 at 19:13
  • $\begingroup$ Excellent answer and website. Thanks! Do you happen to still have the code for solving 4x4x4? It would be interesting to see. Since bruteforcing the 45**4 possibilities might not be the fastest solution. $\endgroup$ – Eric Duminil Jul 17 '20 at 22:25

Here is another documented colouring to this puzzle step by step



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