The box contains blue and red balls. Some of the balls have a radius of 3 cm, others 5 cm.

The box contains blue and red balls. Some of the balls have a radius of 3 cm, others 5 cm. Are there two balls of different colors in the box, which differ in size?

Suppose, for the first time, they pulled out a blue ball with a radius of 3 cm, denote c3. Then, next you need to pull out a red ball with a radius of 5 cm, k5. Suppose that there are no such balls of red color and they are all of radius 3. But by condition, there are balls of different radii. Then, if there are no red balls with a radius of 5 cm, then blue balls must be available with such a radius. And, at least, there is a pair of k3-c5 and, therefore, in the box there are two balls of different colors, which differ in size.