The repetition trick

Pick any sequence of moves and repeat it from a solved cube. Sooner or later the cube is solved again. This works for every sequence, because the cube has a finite number of positions. The number of repeats it takes is called the sequence's order.

R U R' U': order 6

R U: order 105

Do R U 105 times, which is 210 turns, and the cube is solved again. Try it while watching TV.

Why it works

Each repeat moves the same pieces round the same loop.

With R U:

• Seven edges travel round a loop of 7, so they're home every 7 repeats.
• Five corners travel round a loop of 5. After 5 repeats they're back in place but twisted, so they need 3 × 5 = 15 repeats to be home and untwisted.
• Everything is home at once after the smallest number that both 7 and 15 divide: 105.

Common mistakes

• One wrong turn. A single mistake means you'll never come back. Count in groups of ten.