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any A in B, 3 points X,Y,Z \in B with AX = AY = AZ = 1, B set of n points

Source: Romania IMO TST 1993 2.3

February 17, 2020
combinatoricscombinatorial geometry

Problem Statement

Find all integers n>1n > 1 for which there is a set BB of nn points in the plane such that for any A∈BA \in B there are three points X,Y,Z∈BX,Y,Z \in B with AX=AY=AZ=1AX = AY = AZ = 1.
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