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Problem 167

Combinatorics Difficulty 1.4 Multiple choice CEMC Gauss (Grade 8) · Canada · 2013

The Summer Olympics are held once every 4 years. During an 18 year period, what is the largest number of Summer Olympics that could be held?

Pick one

Official solution

Since Lan and Mihai are seated beside each other, while Jack and Kelly are not, the only possible location for the remaining chair (Nate’s chair) is between Jack and Kelly, as shown. Therefore, the 2 people who are seated on either side of Nate are Jack and Kelly.

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