1994 AMC 8 Problem 21
Attempt Problem 21 of the 1994 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1994 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
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: C
Small hint:
Consider the worst case: how many gumballs can you draw with at most three of each color?
Big hint:
Each color has at least three available, so you could draw three of each before the next one forces a fourth
Solution:
In the worst case, a person could draw red, white, and blue, which is gumballs, without yet having four of any color.
The next (tenth) gumball must match one of these colors, giving four of that color. So gumballs are needed.
Thus, the correct answer is C .
Problem 21 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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