What do you think the limit is for "beginners can figure it out"?

[simontiger]

Puzzle	Positions	Maximum moves to solve optimally	Difficulty
3x3	43,252,003,274,489,856,000	20	Around the middle of the line
1x2x2	6	3	Stupidly easy

There must be some point in between above which beginners would get stuck, but below which beginners could figure out by either putting only a little thought into it or just turning randomly. What do you think that is?

 

[DGCubes]

Good question! Unfortunately it's more complicated than just number of positions and maximum number of moves to solve optimally. For example:

Puzzle	Positions	Maximum moves to solve optimally	Difficulty
1x1x100	401,734,511,064,747,568,885,490,523,085,290,650,630,550,748,445,698,208,825,344	99	Trivial

This question also definitely changes from solver to solver. Some people naturally have a great intuition for twisty puzzles and could figure out a 3x3 on their own, and others could spend days with a 2x2 and have no luck.

This question could have a more direct answer if you limit it to turning randomly (in which case, a 1x1x100 would be essentially impossible). If you do one random turn every second for a relatively long human lifespan of 100 years, you could go through just over 3 billion turns. (Keep in mind that not all positions you go through will be unique, so this wouldn't guarantee that you'd solve a puzzle with 3 billion permutations.) I'm assuming nobody wants to spend their lives that way, so if we limit it to a more reasonable time investment of 100 hours, you could go through 360,000 permutations. You can certainly play around with the numbers from here, but unfortunately I don't think there's any great way to determine whether a puzzle is solvable by beginners without knowing the specific person.

 

[qwr]

Maybe you could approximate difficulty by how many "overlapping moves" there are and how much jumbling there is. Maybe the size of the minimal group presentation is some kind of measure of complexity.