Welcome to the staging ground for new communities! Each proposal has a description in the "Descriptions" category and a body of questions and answers in "Incubator Q&A". You can ask questions (and get answers, we hope!) right away, and start new proposals.
Are you here to participate in a specific proposal? Click on the proposal tag (with the dark outline) to see only posts about that proposal and not all of the others that are in progress. Tags are at the bottom of each post.
Post History
There are 6 permutations of the numbers 1, 2, 3. They are: 123 132 213 231 312 321 The goal is to make a string (as short as possible) using the digits 1, 2 and 3 so that each of the abov...
#1: Initial revision
by
will.octagon.gibson
·
2026-08-04T01:26:56Z (about 1 month ago)
Find the shortest possible string containing all permutations of 1, 2, 3
There are 6 [permutations](https://en.wikipedia.org/wiki/Permutation) of the numbers 1, 2, 3. They are: ```text 123 132 213 231 312 321 ``` The goal is to make a string (as short as possible) using the digits 1, 2 and 3 so that each of the above 6 permutations occur at least once in consecutive positions in the string. The sample string below contains all 6 permutations. The string is 12 digits long but there are shorter strings that contain all 6 permutations. As examples, the permutation 213 occurs in the positions marked AAA and the permutation 123 occurs in the positions marked BBB. ```text AAA BBB 132132323123 ``` What is the shortest string that satisfies the above conditions? --- I know what the shortest string length is. If you post a correct string with that shortest possible length, I plan to upvote your answer. If you also give a proof that your answer is minimal which I find easy to understand, I plan to mark your answer as **Works for me.**