2001 CEMC Pascal Problems/Problem 12

Problem

A bag contains $20$ candies: $4$ chocolate, $6$ mint, and $10$ butterscotch. Candies are removed randomly from the bag and eaten. What is the minimum number of candies that must be removed to be certain that at least two candies of each flavour have been eaten?

$\text{ (A) }\ 6 \qquad\text{ (B) }\ 10 \qquad\text{ (C) }\ 12 \qquad\text{ (D) }\ 16 \qquad\text{ (E) }\ 18$

Solution

One could eat all of the butterscotch and mint candies before eating the chocolate candies, and they would then have to eat $2$ extra chocolate candies in order to be certain that at least two candies of each flavor have been eaten.

This means that $10 + 6 + 2 = \boxed {\textbf {(E) } 18}$ candies have to be eaten in order to be certain that at least two of each flavor has been eaten.

~anabel.disher

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2001 CEMC Pascal Problems/Problem 12

Problem

Solution