# Problem 9.2 (7 points)

In a bag, there are 70 balls that differ only in color: 20 red, 20 blue, 20 yellow, and the rest are black and white.

What is the minimum number of balls that need to be drawn from the bag, without seeing them, to ensure that among them there are at least 10 balls of the same color?
# Solution:

By drawing 37 balls, we risk getting 9 red, 9 blue, and 9 yellow balls, and we won't have ten balls of one color. If we draw 38 balls, the total number of red, blue, and yellow balls among them will be at least 28, and the number of balls of one of these colors will be at least ten (since $28 > 3 \cdot 9$).

| Criteria | Points |
| :--- | :---: |
| Complete solution | 7 |
| Answer without justification | 1 |
| Incorrect answer | 0 |

Answer: 38 balls