A very quick skim of the article immediately brought these to mind: https://en.wikipedia.org/wiki/De_Bruijn_sequence https://en.wikipedia.org/wiki/De_Bruijn_seq

A very quick skim of the article immediately brought these to mind: https://en.wikipedia.org/wiki/De_Bruijn_sequence https://en.wikipedia.org/wiki/De_Bruijn_sequence (Edit: I don't know if it's true but I've heard a story that these sequences were actually used by car thieves to cycle through all N-digit combinations with maximal efficiency. Who says maths isn't useful) Now, are there any combinatorists here who would be willing to have a private chat with me about something I stumbled upon a few years ago? Almost certainly well known, but I can't find any prior art and I've looked hard.