# When $$\mbox{RU}$$ coming back to me?

Algebra Level pending

Now, let's spice things up a bit. In the last problem, we did $$\mbox{R}_2$$ and $$\mbox{U}_2$$ moves to transform the cube. This time, let's do $$\mbox{R}$$ and $$\mbox{U}$$ moves (only one clockwise quarter turn each time). If we perform $$\mbox{R}$$ followed by $$\mbox{U}$$, we call that the $$\mbox{RU}$$ permutation.

How many $$\mbox{RU}$$ permutations must we perform before the $$2\times 2\times 2$$ cube is back to its original state?

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