Finding algorithms to solve mechanical puzzles in general?

[skan]

I was wondering how people find the algorithms to solve mechanical puzzles such as Rubik, Megaminx, Gear Cube...

How do they find it?
Are they specially intelligent?
Just by a brute force process?
With complex mathematics?
With computers?
A mix of all those methods?

I guess they try simple movements and annotate how every piece changed.
Later they try to compose several of these movements and try to see if it can be reduced in some way to get the same result.
And then they try to find useful combinations maybe with the help of a computer.

 

[biscuit]

First you try to reduce it to something that is easier to understand or close to something you know. Then you basically try to solve as much as you can. Then it's trial and error to figure out how you can solve small amounts of pieces without messing others up, many times in the form of commutators.

There may be other techniques, but this is enough to figure a puzzle out.

Or you can just use a computer.

 

[Rcuber123]

U can try using commutaters and conjugates

 

[shadowslice e]

You may find this thread interesting. Note that they are explaining the algorithms which were generated by a computer however.

 

[Cale S]

Computer programs like ksolve can be used to generate algorithms for basically any puzzle, even ones that don't exist. But a lot of permutation puzzles can be solved with knowledge of other puzzles and constructing commutators and conjugates.

 

[bubbagrub]

I recommend searching for Tony Fisher's videos on how he figured out solving the 3x3 and 4x4. They're very informative and interesting. And a little mind-blowing...

 

[stoic]

This recent thread over on TP covers the topic in a bit of detail.

Edit: ah ok. I see you've already been over there.