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If this puzzle reminds you of a Rubik's cube that is not a coincidence. The mathematical structure of both puzzles is essentially the same. The moves in both p

by lisper 4y ago

If this puzzle reminds you of a Rubik's cube that is not a coincidence. The mathematical structure of both puzzles is essentially the same. The moves in both puzzles form a non-abelian group, which is the source of the challenge. See http://web.mit.edu/sp.268/www/rubik.pdf http://web.mit.edu/sp.268/www/rubik.pdf In fact, a fun meta-puzzle is to find a three-dimensional analog to this two-dimensional puzzle.

bradrn 4y ago
> In fact, a fun meta-puzzle is to find a three-dimensional analog to this two-dimensional puzzle. I believe this puzzle is equivalent to a Ehovxf phor ba n gbehf (rot13).
- malf 4y ago
  It’s always a gbehf
  - enchiridion 4y ago
    Can someone explain that notion?
    - danbruc 4y ago
      No notation, ROT13 encryption [1]. [1] https://en.wikipedia.org/wiki/ROT13 https://en.wikipedia.org/wiki/ROT13
theideaofcoffee 4y ago
My first thought was the same, “ah it’s just a group puzzle like a rubik’s”. In my case, understanding the math doesn’t make up for me being completely useless in solving it.
- Jill_the_Pill 4y ago
  Whereas I solved it by instinct and am still not sure how. Maybe it is better to be lucky than good!
ICodeSometimes 4y ago
TIL! It definitely struck a cord with my old rubik's cube solving days
abnry 4y ago
It might be helpful to note that the moves form a group, but the puzzle itself is the group action of this group on the cubes/squares/pieces. In this context it reveals the usefulness of commutators, which are moves of the form ABA'B', where A and B are some sequence of moves and ' denotes inverse. In general A and B aren't commutative, but with respect to a subset of the pieces, the actions of A and B are effectively commutative, so ABA'B' will do nothing to those pieces. Which means you can get some simple permutation control over the remaining (usually much smaller) pieces of the puzzle.
yuchi 4y ago
A 3d dimension version would require wrapping… I wonder if such a shape exists! (I don’t want to spoil this micro challenge more than I already did)
taeric 4y ago
Fun. I have a blog I wrote years ago that had fun seeing a Rubik's cube as permutations. I can see how that could map somewhat to this. I should pick that back up. Post was: https://taeric.github.io/cube-permutations-1.html https://taeric.github.io/cube-permutations-1.html
bombcar 4y ago
With both, a key can be learning how to "swap" two pieces without modifying the others around them - once you have that worked out, you basically can solve it even if not in the most efficient manner possible.
GuB-42 4y ago
And the meta-meta puzzle is, once you found a 3D equivalent, make it a physical object. Both the "easy/medium" and "hard" puzzles look tricky to make in their own way, my gut feeling is that he "hard" puzzle is the easier one to design.
deleted 4y ago
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by lisper 4y ago

bradrn 4y ago

> In fact, a fun meta-puzzle is to find a three-dimensional analog to this two-dimensional puzzle. I believe this puzzle is equivalent to a Ehovxf phor ba n gbehf (rot13).

malf 4y ago
It’s always a gbehf
- enchiridion 4y ago
  Can someone explain that notion?
  - danbruc 4y ago
    No notation, ROT13 encryption [1]. [1] https://en.wikipedia.org/wiki/ROT13 https://en.wikipedia.org/wiki/ROT13

theideaofcoffee 4y ago

My first thought was the same, “ah it’s just a group puzzle like a rubik’s”. In my case, understanding the math doesn’t make up for me being completely useless in solving it.

Jill_the_Pill 4y ago
Whereas I solved it by instinct and am still not sure how. Maybe it is better to be lucky than good!

ICodeSometimes 4y ago

TIL! It definitely struck a cord with my old rubik's cube solving days

abnry 4y ago

It might be helpful to note that the moves form a group, but the puzzle itself is the group action of this group on the cubes/squares/pieces. In this context it reveals the usefulness of commutators, which are moves of the form ABA'B', where A and B are some sequence of moves and ' denotes inverse. In general A and B aren't commutative, but with respect to a subset of the pieces, the actions of A and B are effectively commutative, so ABA'B' will do nothing to those pieces. Which means you can get some simple permutation control over the remaining (usually much smaller) pieces of the puzzle.

yuchi 4y ago

A 3d dimension version would require wrapping… I wonder if such a shape exists! (I don’t want to spoil this micro challenge more than I already did)

taeric 4y ago

Fun. I have a blog I wrote years ago that had fun seeing a Rubik's cube as permutations. I can see how that could map somewhat to this. I should pick that back up. Post was: https://taeric.github.io/cube-permutations-1.html https://taeric.github.io/cube-permutations-1.html

bombcar 4y ago

With both, a key can be learning how to "swap" two pieces without modifying the others around them - once you have that worked out, you basically can solve it even if not in the most efficient manner possible.

GuB-42 4y ago

And the meta-meta puzzle is, once you found a 3D equivalent, make it a physical object. Both the "easy/medium" and "hard" puzzles look tricky to make in their own way, my gut feeling is that he "hard" puzzle is the easier one to design.

deleted 4y ago

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