What is the best sequence to tighten the lug nuts on a wheel with N nuts?

Nuts are numbered [0,N) as you travel around the circle, and we’d like to output the list of nut indexes to tighten, in order. For N=4, we’d tighten [0,2,1,4], although there are many equivalent solutions due to the inherent symmetry. For N=5, we have [0,2,4,1,3].

This problem actually came up when I was trying to pick a deterministic “maximally distant sequence” of colors for a visualization that I was doing. There are answers good enough (or better) for my visualization problem, but I feel like the question is an interesting one. One thing that probably needs doing is defining the objective function (i.e., “maximally distant”) in a more formal way.

This post is intended to shame my future self into looking at it again, one day!

Tags: math