The 9 cubes forming one face can be rotated through 45 rotations. There are 43,252,003,274,489,856,000 different arrangements of the small cubes, only one of these arrangements being the initial position where all colors match on each of the six sides. Solving this puzzle involves both sides of the brain as you must be able to previsualize spatially the final result while you remember where you've been in the sequence of rotations. Though a very difficult puzzle, it is a good exercise for brain flexing whether you accomplish the final result or not. No one really knows when Peg solitaire was invented.
Some stories trace it to prisoners during the French Revolution.
Most likely the game is even older. There are probably variations in all cultures dating to antiquity. Play is simple, yet challenging. This challenges both sides of the brain for as you spatially move around the board you need to remember which strategies you have used before. It utilizes both logical and analogical kinds of thought.