New blog post: Counting paths in convex polygons,

A simple coloring-based explanation for why there are exactly \(n2^{n-3}\) non-crossing paths through all points of an \(n\)-gon, and exactly \(\tfrac{n}{4}(3^{n-1}+3)\) through some of the points (counting a single point as a path).

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In the first diagram, should the top-right blue point be red (or the last two path steps changed)?

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