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Proposed solution123121321 for 9 symbols. Reasoning The first three symbols should be a permutation because otherwise we can trim the first symbol without losing any permutation. Without loss of ...
#1: Initial revision
by
Peter Taylor
·
2026-08-04T08:05:23Z (about 1 month ago)
<details><summary>Proposed solution</summary><code>123121321</code> for 9 symbols.</details> <details><summary>Reasoning</summary> The first three symbols should be a permutation because otherwise we can trim the first symbol without losing any permutation. Without loss of generality we can start with `123`. Given a prefix, call a one-symbol continuation of it "good" if it contributes a new permutation. The only good continuation of `123` is `1`, and the only good continuation of `1231` is `2`. There are no good continuations of `12312` because `123` is already contained in the string. So we have three permutations in five symbols. The other three permutations can similarly be done in five symbols, and by choosing to start at `2` we can overlap and save a symbol, giving nine symbols in total. The result has only one three-symbol substring which doesn't contribute a necessary permutation: the central `121`. To improve on that would require starting with a permutation and making five good extensions, and we've already seen that this is impossible. </details>