Problem:
A box contains red balls, green balls, yellow balls, blue balls, white balls, and black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 15 balls of a single color will be drawn?
Answer Choices:
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Solution:
We try to find the worst case scenario where we can find the maximum number of balls that can be drawn while getting of each color by applying the pigeonhole principle and through this we get a perfect guarantee. Namely, we can draw up to red balls, green balls, yellow balls, blue balls, white balls, and black balls, for a total of balls, without drawing balls of any one color. Drawing one more ball guarantees that we will get balls of one color - either red, green, or yellow. Thus, the answer is .
The problems on this page are the property of the MAA's American Mathematics Competitions