A combi salad from mathematical olympiad treasures
Posted: Tue Dec 22, 2020 10:08 pm
Let n and k be two natural numbers and let S be a set of n points such that
(a) no three points of S are collinear.
(b) for any point P of S there are at least k points of S which are equidistant from P.
Prove that k<1/2+(2n)^(1/2)
(a) no three points of S are collinear.
(b) for any point P of S there are at least k points of S which are equidistant from P.
Prove that k<1/2+(2n)^(1/2)