7.2.2

Summary:

This puzzle consists of 6 pieces, namely A, B, C, D, E and F.

Clicking on a piece flips an area containing 4 pieces.
Clicking inner pieces (A,B and C) flips the area horizontally.
Clicking outer pieces (D,E and F) flips the area vertically.
Sequences [A,D], [B,E], [C,F] rotate the area by 180°.

→ [A] →

→ [D] →

Solved states:

There are these 12 solved states.

Mathematical facts:

· The permutation group of pieces is S6.
· Any piece can be at any of 6 places, and can have any of 12 orientations(2 faces × 6 rotations).
· The sum of twists is always n×120°(0°,120°,240°).
· The number of flipped pieces is always even(0,2,4,6).
So the total number of possible scrambles is: (6!) × ((2*6)^6)/2/2 = 537,477,120.