This problem was solved by Branko Grunbaum, with the solution described in the October 1998 issue of Geombinatorics, a small journal by Alexander Soifer at the University of Colorado. Let X(n) be the set of possible numbers of intersections and x(n) be the maximum of X(n) for a given n. For odd n, x(n)=n(n-3)/2 and X(n) is the set of all integers from 0 to x(n) except x(n)-1. For even n, x(n)=1+n(n-4)/2 and X(n) is the set of all integers from 0 to x(n). His proof is somewhat complicated. The paper illustrates X(3) through X(6). Steve Gray ----- Original Message ----- From: "David Wilson" <davidwwilson@comcast.net> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Saturday, April 16, 2005 1:45 AM Subject: [math-fun] Polygon problem

In a self-crossing polygon of n vertices, what is the maximum number of possible crossings?

- David W. Wilson

"Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"

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