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 :)