Rethinking Difficulties ! a first trial.
There must be a way to *calculate / systematize difficulties.
To make things comparabe, lets use the one and only puzzle really EVERYONE knows & (most) love.
Here a clearly NOT mathematical approach, but more a conceptual one :
The rubiks cube :
- Shape : it's 3D - around a corned. You can't visually see whats happening on the other side as you make a move.
How much can you NOT see ? - Global Overlap : One move changes pieces on other planes lets call them rotators, to be consistent with trinagon .
* How many other rotators of the whole are influenced by the one turn ?
* How many pieces of each other rotator are switched / moved ?
* And maybe : How many pieces of the whole are NOT influenced by a single move ? - Local Overlap : How many of the neighbouring rotators pieces are moved ?
neighbouring rotators are those that share pieces.
How many pieces are overlapping between shared rotators should maybe also enter the calculation ? - Restability & Interchangeability : These two seem to be good concepts derived from the 'Overlaps'.
Restability is a global affair : How many pieces can be left alone while the others are manipulated ?
Interchangeability is local but in measured relation : How many pieces can be exchanged between two neighbouring rotators while still resting the others. - Other considerations :
How many single piece 'states' (orientation) exist dependent or independent ?
In other words : How many orientation can each piece have on a certain spot & are they all available or interdependent ? - Cube specific : The 3x3 cube is actually two puzzles wrapped into one. The edges & the corners.
The 2x2 cube is a corner-only and much simpler puzzle.
This is only a start. Any clarity shall be published here :)