Hints for working out the solutionEdit
As a web search reveals that there are at least two different colour schemes (one on the cube owned by RedKB, another on the cubes owned by Jaap Scherphuis and by the author of this edit), it is not advisable to talk in terms of specific colours as is too-often done. Hence the description below will be in terms of colour groups.
There are three kinds of groups of one colour:
- The first group contains two corners.
- The second type (six groups) has one centre, one corner, and one edge of that colour.
- The third type (the remaining two colours) has three edges.
It's fairly obvious that the two identical corners must be at the ends of one of the cube's main diagonals, otherwise there would be at least one face containing both of them. Further analysis shows that the six groups of type 2 must each have its three pieces lying on a plane which cuts through the cube along the line of the face diagonal which includes that group's centre and one of the corners of group 1, and of the opposite face's diagonal which includes the other group-1 corner; and the remaining six edges are the two type-3 groups alternating (forming a hexagonal ring).