### 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 :)