## Task 3 - 120523

In a box, there are a total of 100 equally sized balls, namely 28 red, 28 blue, 26 black, 16 white, and 2 green.

Ulrike is supposed to take a number of balls out of this box in the dark (so she cannot see the color of any of the balls she takes out). She should choose this number in such a way that among the balls taken out, at least 9 must have the same color.

What is the smallest number of balls Ulrike can choose to fulfill this task?
In the worst case, Ulrike can initially take out 8 red, 8 blue, 8 black, 8 white, and the two green balls.

If she then takes out one more ball in addition to these 34 balls, this ball can only be one of the four colors red, blue, black, or white.

In this case, Ulrike will thus have 9 balls of the same color.

The smallest number of balls for which this is certainly the case is therefore 35.

## Solution adopted from $[5]$