Octacube (by Mindope) is a type of mind-teaser puzzle made up of eight cubes with colors on the faces. The object of the puzzle is to arrange the eight cubes into a 2×2×2 cube such that all faces show the same color on the inside and all external colors which magneticly touch are the same color. There are seven colors in the puzzle, and each of the eight cubes shows the seven colors, one per face.
There is some clever mathematics behind this puzzle. It turns out that for the above stated constraints, there are only five possible solutions, and they happen to made up of the same eight cubes. It also turns out that these eight cubes must all have in common four pairs of adjacent colors. This condition, in fact, is both necessary and sufficient to yield the set of cubes giving the two solutions.