- Thread starter
- Admin
- #1

- Jan 26, 2012

- 4,198

-----

Given $n$ points in the plane, any listing (permutation) $p_1, p_2,\dots,p_n$ of them determines the path, along straight segments, from $p_1$ to $p_2$, then from $p_2$ to $p_3,\dots,$ ending with the segment from $p_{n-1}$ to $p_n$. Show that the shortest such broken-line path does not cross itself.

-----

Remember to read the POTW submission guidelines to find out how to submit your answers!