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China Team Selection Test 2013 TST 2 Day 1 Q3

Source:

April 1, 2013
geometryparallelogramcombinatorial geometrycombinatorics proposedcombinatorics

Problem Statement

Let AA be a set consisting of 6 points in the plane. denoted n(A)n(A) as the number of the unit circles which meet at least three points of AA. Find the maximum of n(A)n(A)