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IMO LongList 1967, Great Britain 3

Source: IMO LongList 1967, Great Britain 3

December 16, 2004

geometrypoint seteuclidean distancemaximizationIMO ShortlistIMO Longlist

Problem Statement

The

n

points

P_1,P_2, \ldots, P_n

are placed inside or on the boundary of a disk of radius 1 in such a way that the minimum distance

D_n

between any two of these points has its largest possible value

D_n.

Calculate

D_n

for

n = 2

to 7. and justify your answer.