There are 15 red, 10 green and 9 white balls in the dark room. jack wants to take a minimal number of balls such that at least 8 of them have the same color. what is the number of balls that he takes?

Jack is considering the "worst case", the case where he is "as unlucky as possible", but which gives him the mathematical certainty that he has picked at least 8 balls of the same color.

what may happen, if Jack is very very unlucky, is that he may pick 7 white balls, 7 green balls and 7 red balls, so 7*3=21 in total.

The 22nd will either be white, green or red, so he will have picked 8 balls of the same color.

22