Clicking one of these points rotates 4 pieces forming a diamond shape around them by 90 °.
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→ [A] → |
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Solved states:
This puzzle has only one of these 3 solved states, depending on its original orientation.
Mathematical facts:
· The permutation group of pieces is the transitive subgroup of S6.
· Any piece can be at any of 6 places, and can
be twisted by n×90°.
· The sum of twists is always (n×360°)
=0°.
So the total number of possible scrambles is:
(5!) ×(4^5) = 122,880.
Solution:
There are only 20,616(≅122,880÷6)solving-wise different scrambles.
Any scramble can be solved within 10 moves, and more than 90% of them, within 6~8 moves.
| moves required | number
of scrambles |
| 0 | 1 |
| 1 | 2 |
| 2 | 9 |
| 3 | 52 |
| 4 | 261 |
| 5 | 1,237 |
| 6 | 4,548 |
| 7 | 9,047 |
| 8 | 5,098 |
| 9 | 359 |
| 10 | 2 |
| total | 20,616 |
