Cubing Conundrum

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A Rubik's Cube is a puzzle in which you turn the faces of a \(3\text{x}3\) block to try and make each of the \(9\) stickers on each face match with each other.

Some have said that now matter how many times they turn the cube, they can't solve it. Some have tried repeating the same algorithm over and over again, but they claim they will never solve it because there are an infinite number of permutations of the cube.

Suppose you have a solved cube. You want to perform a certain algorithm over and over again until the cube once again reaches a solved state, no matter how long it takes. How many algorithms exist such that if you perform them over and over again, you will never reach a solved state again?

\(\textbf{Note:}\) If you think there are more than \(999\) such algorithms, type \(999\) as your answer.


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