a symmetry of a system is an operation done to a system, such as rotation or displacement, that leaves the system fundamentally unchanged. a symmetry also provides a rule for how something should always act unless acted on by an outside force. an example is a rubik's cube. if we take a rubik's cube and scrambled it by making whatever moves we want, it is still possible to solve it. since each move we make still leaves the rubik's cube solvable, we can say that these moves are 'symmetries' of the rubik's cube. together, they form what we call the symmetry group of the rubik's cube. making any of these moves doesn't change the puzzle, always leaving it solvable. but, we can break this symmetry by doing something like taking the cube apart, and putting it back together in a completely wrong way. no matter what moves we try now, it is not possible to solve the cube. breaking the cube apart and putting it back together in the wrong way is the 'outside force': without this outside force, nothing we do to the cube makes it unsolvable. the symmetry of the rubik's cube is that it stays solvable whatever moves we make, as long as we do not take apart the cube.