Congratulations to this week's winner
Jillian Martens
Further solutions were submitted by Philippe Fondanaiche, Nancy Schwarzkopf,
Lou Cairoli, Al Zimmermann, Scott Powell, Rick Bischoff, Burkart Venzke,
Steven McEwan, Dane Brooke, Sudipta Das, Tim Riehle, Paul Botham.
Since no three diagonals ever intersect in a point, each
intersection in the interior of the n-sided polygon is uniquely
detemined by two line segments whose endpoints are vertices of the
polygon. This gives a one-to-one correspondence between interior
intersections and sets of four vertices of the polygon. The answer
is then given by the combinatorial number C(n,4) = n!
/ (4!(n-4)!) =
n(n-1)(n-2)(n-3)/24.
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