Question 3
A cube can be rotated about any of the three axes a, b and c shown.
(i) A is a 90-degree turn about axis a in the arrow direction.
(ii) B is a 90-degree turn about axis b in the arrow direction.
(iii) C is a 90-degree turn about axis c in the arrow direction.
(iv) Consecutive letters are performed from left to right: AB means A followed immediately by B.
(v) Powers repeat a move, so $A^2$ means A twice.
One face is marked IMSO.
(a) If IMSO starts on the front, where will it be after $A^3B$?
(b) If IMSO is on the bottom after ABC, where was it before those moves?
(c) Start with IMSO on the front. Write as many sequences as you can that return this face to the front, using each of A, B and C at most twice.
(i) A is a 90-degree turn about axis a in the arrow direction.
(ii) B is a 90-degree turn about axis b in the arrow direction.
(iii) C is a 90-degree turn about axis c in the arrow direction.
(iv) Consecutive letters are performed from left to right: AB means A followed immediately by B.
(v) Powers repeat a move, so $A^2$ means A twice.
One face is marked IMSO.
(a) If IMSO starts on the front, where will it be after $A^3B$?
(b) If IMSO is on the bottom after ABC, where was it before those moves?
(c) Start with IMSO on the front. Write as many sequences as you can that return this face to the front, using each of A, B and C at most twice.