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, 2004

Combinatorics Difficulty 2.0 Junior Find the answer Canada

There are $13$ trees on one side of the street on Trina's way from her house to school. Today, on her way to school, Trina put a chalk mark on every other tree, starting with the first she passed. When she goes home from school, she will put a chalk mark on every third tree, again starting with the first one she passes. By the time Trina arrives at home, how many of the $13$ trees will not have a chalk mark on them?

(A) $6$ (B) $4$ (C) $8$ (D) $2$ (E) $7$

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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.