Why do I love 2015 so much #5

Discrete Mathematics Level 4

We take a \(4×4×4\) Rubik's cube in the solved state and with that configuration, we perform a sequence of moves \(R'FRU\), 2015 times in the same order to bring about another configuration (say \(A\)) in the cube.

How many times do we have to perform the same sequence of moves \(R'FRU\) so as to bring the cube from the configuration \(A\) into the solved state again?

Details and Assumptions

  • \(R' \rightarrow\) Outer Right layer rotated anti-clockwise.

  • \(F \rightarrow\) Outer Front layer rotated clockwise.

  • \(R \rightarrow\) Outer Right layer rotated clockwise.

  • \(U \rightarrow\) Outer Upper layer rotated clockwise.

This problem is a part of this set.

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