Doing it right wrongly
A box contains 100 balls of the following colours: 28 red,17 blue, 21 green, 10 white, 12 yellow and 12 black. What is the smallest number such that any balls drawn from the box will contain at least 15 balls of the same colour?
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The worst case scenario you will get so no color is consisted of 15 balls is 10 white, 12 yellow, 12 black, 14 red, 14 blue, 14 green with total of 76 balls. Next ball you pull must be either red, green or blue, maikng them 15. so the least n satisfy is 7 6 + 1 = 7 7 balls.