7.4.2

Summary:

This puzzle consists of 12 hexagonal pieces.
Clicking one of three central pieces flips the piece and surrounding 6 pieces,
around the axis connecting the center of the piece and the nearest corner or edge of the hexagon.

Solved states:

There are 6 visiblly different solved states, two solutions below and their ∓120° rotations.

Reflections of above solutions are not possible, unless the initial state is one of them( this is not the case).

This comes from the parity issue explained below.

Mathematical properties:

· The permutation group of pieces is S12.
· Any piece can be at any of 12 places, can be flipped or not, and and can be rotated by (0~5)×120°.
· The parity of the sum of twists of pieces coincides with the permutation parity of the pieces N×360°=0.
· Therefore, the total number of possible scrambles is (12!)×(12¹²)÷2=2,135,413,190,237,670,604,800.