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Problem 274

Combinatorics Difficulty 1.5 Multiple choice CEMC Gauss (Grade 8) · Canada · 2012

Yelena recites $P, Q, R, S, T, U$ repeatedly (e.g. $P, Q, R, S, T, U, P, Q, R, \dots$ ). Zeno recites $1, 2, 3, 4$ repeatedly (e.g. $1, 2, 3, 4, 1, 2, \dots$ ). If Yelena and Zeno begin at the same time and recite at the same rate, which combination will not be said?

Pick one

Official solution

Since 1 mm of snow falls every 6 minutes, then 10 mm will fall every $6\times10=60$ minutes. Since 10 mm is 1 cm and 60 minutes is 1 hour, then 1 cm of snow will fall every 1 hour. Since 1 cm of snow falls every 1 hour, then 100 cm will fall every $1\times100=100$ hours.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.