This iterative process produces a chain of different sequences
which is actually a sequence of sequences . Start with short
sequences of small numbers so that you can easily produce a
chain of sequences and notice patterns. Look out for sequences that
have already occured earlier in your chain.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.