## Task 5 - 030725

In a box, there are 70 balls, namely 20 red, 20 green, 20 yellow, and the rest are black or white. Brigitte is supposed to take out as many balls from this box in the dark so that among them, there are certainly at least 10 balls of the same color.

How many balls does she have to take out at least? Justify your answer!
She must take 38 balls.

In the worst case, Brigitte can first take out the 10 black or white balls and 9 balls of each color, a total of 37 balls. If she now takes out one more ball, she will always have at least 10 balls of the same color among these 38 balls.

Solutions of the II. Round 1963 adopted from [5]

### 4.5.3 III. Round 1963, Class 7