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Problem 203

Combinatorics Difficulty 1.5 Multiple choice CEMC Gauss (Grade 7) · Canada · 2017

Five students ran a race. Ryan was faster than Henry and Faiz. Henry was slower than Faiz. Toma was faster than Ryan but slower than Omar. Which student finished fourth?

Pick one

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Official solution

Henry was slower than Faiz and thus finished the race behind Faiz.

Ryan was faster than Henry and Faiz and thus finished the race ahead of both of them.

From fastest to slowest, these three runners finished in the order Ryan, Faiz and then Henry.

Toma was faster than Ryan but slower than Omar.

Therefore, from fastest to slowest, the runners finished in the order Omar, Toma, Ryan, Faiz, and Henry.

The student who finished fourth was Faiz.

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