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MathNet 2026 — Part 01 Question 172

Math Olympiad Vault · MathNet 2026 — Part 01

Question 172

The course of an athlete - an athlete decided to do a race of $15~\mathrm{km}$. It started running $5~\mathrm{km}$ in a southerly direction, then turned eastward, running further $5~\mathrm{km}$ and again turned to the north, running the remaining $5~\mathrm{km}$. After this journey, he found, to his amazement, that he was at the point where he had left. Discover two possible points on the globe from which this athlete may have started his race.