MathDB

Find all triples

(a, b, c)

of positive integers with

a+b+c = 10

such that there are

a

red,

b

blue and

c

green points (all different) in the plane satisfying the following properties:

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for each red point and each blue point we consider the distance between these two points, the sum of these distances is

37

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for each green point and each red point we consider the distance between these two points, the sum of these distances is

30

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for each blue point and each green point we consider the distance between these two points, the sum of these distances is

1

Problem Statement