Equilateral triangle's perimeter
Geometry
Level
3
Each point on the perimeter of an equilateral triangle is colored either red or yellow.
Does there exist a right triangle whose 3 vertices have the same color?
Cannot be determined
Yes, there always exists
No, there never exists
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1 solution
Since there are seven points on the triangle and two colors to choose.By pigeon hole principle there exist at least four points with the same color.On each line there is a maximum of three points. The worst case scenario is when three of the four points lie on a same line .Since there is another point with the same color we can make a triangle by placing it on the other side