number of good circles is n
Source: China TST 1991, problem 3
June 27, 2005
invariantinductioncombinatorial geometrycombinatorics unsolvedcombinatorics
Problem Statement
points are given in the plane, any three non-collinear and any four non-concyclic. If three points determine a circle that has one of the remaining points inside it and the other one outside it, then the circle is said to be good. Let the number of good circles be ; find all possible values of .