5

Part of 2012 IMAC Arhimede

Problems(1)

3n points on a circuference, n arcs of lenght 1, no of length 2, n of lengths 3

Source: IMAC Arhimede 2012 p5

On the circumference of a circle, there are

3n

colored points that divide the circle on

3n

n

of which have lenght

1

n

of which have length

2

and the rest of them have length

3

. Prove that there are two colored points on the same diameter of the circle.

combinatoricscombinatorial geometryarccircle