Question

В ящике 28 красных 20 зеленых 12 желтых 20 синих и 10 белых шариков.Какое наименьшее количество шариков надо вытащить не заглядывая в ящик чтобы среди вытащенных шариков обязательно оказалось не менее 15 одноцветных шариков

Answer 1

В самом плохом случае мы вынем 12 желтых, 10 белых, 14 красных,
14 зеленых, и 14 синих. Всего 12+10+3*14 = 22+42 = 64.
65-ый шар будет или красным, или зеленым, или синим, то есть 15-ым определенного цвета.
Ответ: 65.

Answer 2

Minimum Number of Balls to be Drawn Without Looking

To ensure that at least 15 balls of the same color are drawn without looking, we can calculate the worst-case scenario for each color. This means we want to minimize the number of balls drawn while maximizing the number of different colors.

The worst-case scenario would be to draw 14 balls of each color and 1 ball of another color. This would result in a total of 5 different colors being drawn, with each color having at least 14 balls. Therefore, the minimum number of balls to be drawn without looking to ensure that at least 15 balls of the same color are drawn is 71.

This calculation is based on the assumption that the distribution of colors in the box is such that the worst-case scenario is realized.

[[SOURCE #1]]