Problem:
A gumball machine contains red, white, and blue gumballs. The least number of gumballs a person must buy to be sure of getting four gumballs of the same color is
Answer Choices:
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Solution:
It is possible to get four gumballs of the same color by buying , or . However, the first nine gumballs might consist of three of each color, so nine gumballs will not guarantee four of the same color. In this case, the tenth gumball must match one of the previous colors, giving four of that color.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions