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?

Question

Gabriella Holden

Mathematics

25 February, 04:50

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?

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Thomas Waller · Answer 1

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.

Answer: 22