Assumethat 2(r+b) points,with r,b N,aredrawnonacircle,equallyspaced(thus,the rays from the center of the circle to any two adjacent points are at an angle of /(r + b) radians). Assume also that 2r of the points are colored red and that the other 2b are colored blue. (You do not get to choose which points get which color.) Must there be at least one rotation of the circle through its center that puts r red points and b blue points on each side of the vertical line through the center? Provide either a proof that there is such a rotation, or a counterexample having no such rotation.