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MathNet 2010 — Part 01 Question 119

Math Olympiad Vault · MathNet 2010 — Part 01

Question 119

Fifteen red, blue and green points are marked on a plane. It is known that the sum of the distances between the red points and the blue points is $51$, the sum of the distances between the red points and the green points is $39$, the sum of the distances between the blue points and the green points is $1$.
How many points of each color are marked? (Determine all possibilities.)