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That's a De Bruijn sequence. See https://en.wikipedia.org/wiki/De_Bruijn_sequence . A example applied to door codes is at http://stefangeens.com/2001-2013/2004/10/the-de-bruijn-code/ . A search for "De Bruijn garage door" finds a couple of examples of what you mentioned.



Thanks for the name, with it I was able to find the article I was thinking of: http://samy.pl/opensesame/




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