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Number of circles

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September 5, 2010
combinatorics unsolvedcombinatorics

Problem Statement

Let 2n+32n + 3 points be given in the plane in such a way that no three lie on a line and no four lie on a circle. Prove that the number of circles that pass through three of these points and contain exactly nn interior points is not less than 13(2n+32).\frac 13 \binom{2n+3}{2}.
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