The box contains blue and red balls, some of the balls have a radius of 3 cm, the rest – 5 cm.

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

Let us denote the balls as follows:

3c – blue with a radius of 3;

5c – blue with a radius of 5;

3k – red with a radius of 3;

5k – red with a radius of 5.

Let’s say there are no two balls of different colors and sizes in the box. Then only balls of this type can lie in the box: 3k, 5k or 3c, 5c, or 5c, 5k, or 3c, 3k. All this contradicts the problem statement. Therefore, there are two balls of different colors in the box, which differ in size.