Problem 8 · 2014 Math Kangaroo
Medium
Logic & Word Problems
casework
Handsome Fritz has a secret e-mail address that is known by only four of his friends. Today he received eight e-mails at this address. Which of the following statements is definitely correct?
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Answer: D — Fritz received at least two e-mails from one of his friends.
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Hint 1 of 2
Spread 8 e-mails among only 4 senders — can they all stay at one each?
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Hint 2 of 2
This is the pigeonhole principle in disguise.
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Approach: pigeonhole on senders
- Eight e-mails come from just four friends.
- If every friend sent at most one, that is at most 4 e-mails — too few.
- So at least one friend must have sent two or more.
- The statement guaranteed true is (D): at least two e-mails come from one friend.
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