I stumbled across this game in Simon Tatham's puzzle app. It's called cube. The description according to the game is:
You have a grid of 16 squares, six of which are blue; on one square rests a cube. Your move is to use the arrow keys to roll the cube through 90 degrees so that it moves to an adjacent square. If you roll the cube on to a blue square, the blue square is picked up on one face of the cube; if you roll a blue face of the cube on to a non-blue square, the blueness is put down again. (In general, whenever you roll the cube, the two faces that come into contact swap colours.) Your job is to get all six blue squares on to the six faces of the cube at the same time.
Attached is a link to a screenshot of the game :
I would like to ask the Math exchange community if there is a known algorithm for solving such a problem as I haven't found anything online.