Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How would you solve the following problem with Discrete Mathematics, and what is the answer?

Suppose there are 5 different types of ice cream you like. How many random samples ice cream must be eaten to guarantee that you have had at least 7 samples of one type?

share|cite|improve this question
Please share with us your thoughts on the problem. – Sasha Dec 6 '12 at 17:29
I don't have any, discrete is impossible – NoDiscrete Dec 6 '12 at 17:32
Hint : You can think of this as a generalization of the pigeon hole principle. – Siméon Dec 6 '12 at 17:39

HINT: You can eat $30$ samples without getting $7$ of the same type; how? What happens if you eat more than that?

share|cite|improve this answer

Hint: If you have eaten $(5)(6)$ samples, you might not have eaten $7$ of any flavour, since you might have eaten $6$ of each dlavour. But anything over that $\dots$. In your answer, you might be expected to mention and use the Pigeonhole Principle.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.