MathDB

for every A, exist 3 points X,Y,Z such that AX = AY = AZ = 1

Source: 1993 Bulgaria NMO, Round 4, p6

July 30, 2021

combinatorial geometrycombinatoricspoints

Problem Statement

Find all natural numbers

n

for which there exists set

S

consisting of

n

points in the plane, satisfying the condition: For each point

A \in S

there exist at least three points say

X, Y, Z

from

S

such that the segments

AX, AY

and

AZ

have length

1

(it means that

AX = AY = AZ = 1