2+ [ Classical combinatorics (other) $]

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 smallest 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?

#
By drawing 37 balls, we risk getting 9 red, blue, and yellow balls each, and there will be no ten balls of one color. If we draw 38 balls, however, the total number of red, blue, and yellow balls among them will be no less than 28, and the number of balls of one of these colors will be no less than ten (since $28>3 \cdot 9$).

## Answer

38 balls.