Problem 10 · 2026 AMC 8
Medium
Logic & Word Problems
ordering
Five runners finished a race: Luke, Melina, Nico, Olympia, and Pedro. Nico finished 11 minutes behind Pedro. Olympia finished 2 minutes ahead of Melina but 3 minutes behind Pedro. Olympia finished 6 minutes ahead of Luke. Which runner finished fourth?
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Answer: A — Luke.
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Hint 1 of 2
The clues compare runners to each other in a tangle. Pick one person as the zero mark and pin everybody's finish time to that single reference — which runner is mentioned most often?
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Hint 2 of 2
Pedro is the natural anchor (he appears in two clues). Put 0 at Pedro and write each other runner as ‘so many minutes behind Pedro,’ then just read the list in order.
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Approach: anchor everyone to one runner, then read the order
- Pin everyone to Pedro at 0 (minutes behind him). Olympia is 3 behind → +3. Melina is 2 behind Olympia → +5. Luke is 6 behind Olympia → +9. Nico is 11 behind Pedro → +11.
- Sorted front to back: Pedro (0), Olympia (3), Melina (5), Luke (9), Nico (11). Fourth across the line is Luke.
- Why this transfers: for any ‘A is ahead/behind B’ ordering puzzle, convert every relative clue into a position on one number line anchored to a single person — the ranking then just falls out by sorting.
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