MathDB

Sixty points, of which thirty are coloured red, twenty are coloured blue and ten are coloured green, are marked on a circle. These points divide the circle into sixty arcs. Each of these arcs is assigned a number according to the colours of its endpoints: an arc between a red and a green point is assigned a number

1

, an arc between a red and a blue point is assigned a number

2

, and an arc between a blue and a green point is assigned a number

3

. The arcs between two points of the same colour are assigned a number

0

. What is the greatest possible sum of all the numbers assigned to the arcs?

Problem Statement