Once is Enough

 

The Strong Men of Titan from Saturn’s largest moon, consider repetition to be a sin. However, they only have 3 sounds that they can make “Kah”, “Brrrr”, and “Umph” (Let’s call them K, B and U for short.) so it is sometimes difficult not to repeat.

Image from Start Trek III courtesy of
www.ex-astris-scientia.org/gallery.htm

What the strong men of Titan mean by repetition is any sequence of sounds that immediately follows the same sequence…  so

UBUBUKUBUKBKUBUKBUKU

is not a sinful utterance because of this:

UBUBUKUBUKBKUBUKBUKU

but is a sinful utterance because of this:

UBUBUKUBUKBKUBUKBUKU

Show that the strong men of Titan make 10 sounds in a row without sinning?

Extensions:

When the evil Strong Men of Titan want to sing an evil chant, they write X utterances on a wheel and whirl it around and around - singing as it spins. Is it possible that they don't sin until they have spun the wheel twice?

The answer is yes for the following wheel of 4 utterances:

Find a larger wheel for which this is true?

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Whenever the Strong Men of Titan drive on their orthogonal highways, they never repeat a sequence of turns. Replace "B,U,K" above with "Forward, Left, Right" to get an idea of how they move. After he begins his journey by moving forward, can a Strong Men of Titan ever return home to his mom?


An example of a strong man trying to return
home to mom (red dot) without sinning.

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What is the largest N by M paragraph (N,M >1) so that no two rectangles sharing an edge have a repetition? The following 6x6 paragraph is sinful because the red rectangles repeat:
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