Order the five runners from four clues

Question

Five runners, Omar, Pia, Mia, Ravi, and Noah, finished a race in some order, with no ties (someone was 1st, someone 2nd, and so on down to 5th). You know four facts: 1. Omar finished immediately ahead of Pia (right in front of her, no one between). 2. Omar finished ahead of Mia, and Mia finished ahead of Noah. 3. Ravi finished neither first nor last. 4. Mia finished immediately ahead of Ravi. What was the finishing order, from 1st to 5th?

Accepted Answer

Two clues glue pairs of runners together. Clue 1 makes an [Omar, Pia] block (Omar directly in front of Pia). Clue 4 makes a [Mia, Ravi] block (Mia directly in front of Ravi). These two blocks share no runner, and together with Noah they account for all five people. So the race is just these three pieces, [Omar, Pia], [Mia, Ravi], and Noah, lined up in some order. Now apply the ordering from clue 2: Omar before Mia, and Mia before Noah. - "Omar before Mia" means the [Omar, Pia] block comes before the [Mia, Ravi] block. - "Mia before Noah" means Noah comes after the [Mia, Ravi] block. Put the p…

Order the five runners from four clues

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