9.2. In a box, there are several (more than three) balls. Each is painted in some color. If you take out any three balls from the box, there will definitely be at least one red and at least one blue among them. How many balls can be in the box
Answer: 4. Solution. In the box, there are no more than two red and blue balls (otherwise, it would be possible to draw three red or three blue balls) and no more than one ball of other colors (otherwise, it would be possible to draw one blue or red ball and two balls of other colors). Therefore, there are no more than five balls in the box, and if there are five, then among them are two blue and two red balls and one of some third color. But then we could draw a ball of the third color and two blue balls. This means that there cannot be five balls in the box. Therefore, there are four: two blue and two red.

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