7.0.7

ABC

Summary:

This puzzle consists of 6 cubic pieces. Clicking one of 4 converging points of 3 cubes rotates 3 pieces by 90° around the edge between two pieces and then translates them to the next place.
After 3 clicks, pieces are at their original place, but twisted by 90°.
· Type A consists of 6 identical pieces with standard cubic puzzle color scheme.
· Type B consists of 3 pairs of 2 identical pieces, each with 6 colors.
· Type C consists of 6 non-identical pieces, each with 4 colors.

Solved states:

· Type A is considered as solved when all pieces have the same orientation. There are 24 solved states correspondig to 24 orientations of cube.
· Types B and C are considered as solved when all 2 adjacent faces of 2 adjacent pieces have same colors. They have both 12 visibly different solutions.

Mathematical properties:

· The permutation group of pieces is A6.
· Any piece can be at any of 6 places, and can have any of 24 orientations.
· Total number of possible scrambles is (6!)÷2×(246)=68,797,071,360.

Solution:

No exhaustive study yet, but for the type A, a simple search program returns several sequences within 5 moves for all scrambles I tried (if a series of moves around the same axis is counted as 1). And there are (1 + 44 + 44×33 + 44×332 + 44×333 + 44×334 = 53,811,165) such sequences. This is much bigger than the number of solving-wise different scrambles (245 = 7,962,624). So, "Any scramble can be solved within 5 moves" would be a good estimate.