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, 2010

Combinatorics Difficulty 2.0 Junior Find the answer Canada

Four friends went fishing one day and caught a total of $11$ fish. Each person caught at least one fish. All of the following statements could be true. Which one of the statements must be true?

(A) At least one person caught exactly one fish. (B) At least one person caught exactly three fish. (C) At least one person caught more than three fish. (D) At least one person caught fewer than three fish. (E) At least two people each caught more than one fish.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.