7.8.1

Summary:

This puzzle consists of 12 hexagonal pieces.
Clicking one of 3 central pieces rotates the area
including the clicked piece and 6 surrounding pieces by 60°

Solved states:

This puzzle is considered as solved when a honeycomb
pattern with 7 distinct-color hexagons appears.
There are 2 solutions as in the right picture.
Since the overall rotation of the puzzle doesn't matter,
in total, there are 6 visibly different solutions.

white center black center

Mathematical properties:

· The permutation group of pieces is S12.
· Any piece can be at any of 12 places, and can be twisted by N×60°.
· The parity of the sum of twist of pieces by 60° coincides always with the permutation parity of pieces .
· So, the total number of possible scrambles is (12!)×(6¹²)÷2=521,341,110,897,868,800.