Unsolvable Rubik's Cube
Have you ever been frustrated after trying to solve the cube and finding it impossible? If you were certain you were using the correct algorithms, there might be an alternate reason for this. Randomly disassembling and reassembling a 3×3 Rubik’s Cube leaves an 11/12 chance of creating an unsolvable reconfiguration.
In cases of other Rubik’s Cube variations with a higher tile count, the chances are even smaller. It is recommended to use a guide in order to reassemble your cube in a solvable configuration. Cubers with experience will only notice that the puzzle is unsolvable when they reach the final steps.
If the GoCube app ‘Invalid scramble’ error appears, first you need to double-check your cube and make sure you entered the color of each field correctly. If you keep getting this message then you’ll have to disassemble and reassemble your cube into the solved position.
The following are parameters that must be oriented correctly in order for the 3×3 to be solvable.
Corner pieces have three possible orientations. It can be oriented correctly, clockwise, or counterclockwise. The sum of corner orientations always remains divisible by 3, no matter how many legitimate turns you make. The first two cases illustrate this case.
Edges have 2 options: they can be oriented correctly or flipped. The third example illustrates this case.
It is possible to place an edge piece or corner piece in the wrong place. The fourth example illustrates this case.
Adding all of these principles together gives us ⅓*½*½= 1/12. In other words, there is a one in twelve chance of randomly arranging a 3×3 Rubik’s Cube correctly.
These images illustrate situations with impossible restickering. The corner example has the orange and yellow flipped. The center example has the white facing up instead of down. The edge piece example shows two colors from faces that are never adjacent.
The possibility of putting your cube together into an impossible configuration is quite high. Be careful to use a reference guide when reconfiguring your cube, and when restickering the best practice is to resticker to a solved state. Good luck reconfiguring your cubes!