1994 AJHSME Problems/Problem 21

Problem

A gumball machine contains $9$ red, $7$ white, and $8$ blue gumballs. The least number of gumballs a person must buy to be sure of getting four gumballs of the same color is

$\text{(A)}\ 8 \qquad \text{(B)}\ 9 \qquad \text{(C)}\ 10 \qquad \text{(D)}\ 12 \qquad \text{(E)}\ 18$

Solution

If a person gets three gumballs of each of the three colors, that is, $9$ gumballs, then the $10^{\text{th}}$ gumball must be the fourth one for one of the colors. Therefore, the person must buy $\boxed{\text{(C)}\ 10}$ gumballs.

See Also

1994 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 20
Followed by
Problem 22
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All AJHSME/AMC 8 Problems and Solutions

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