> If a television series has just three episodes, there are six possible orders in which to view them: 123, 132, 213, 231, 312 and 321. You could string these six sequences together to give a list of 18 episodes that includes every ordering, but there’s a much more efficient way to do it: 123121321.
And with 7 substrings of length 3, it's provably minimal, since making every 3-substring a permutation of 123 forces every element after the first 2. Assuming without loss of generality that it starts with 1 2, it is forced to start with
1 2 3 1 2 3
but there already repeats the same permutation. So one substring must be wasted (in the article this is phrased as having to traverse one higher cost edge in the corresponding graph).
that ...,1,2,1,.. in the middle bothers me, nobody wants to watch three in a row that does not include all three, i'd rather have a duplicate triplet, or at least include the case as another potential bound, or classes of orderings where perhaps some numbers of elements have these defects while others don't.
