Puzzle 15: The Weighted Verdict
Puzzle Walkthrough
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Exactly one of these is true about Miles: he held the Blue token or he attempted the Rope Puzzle. So for Miles, Blue and Rope Puzzle cannot both be true and cannot both be false.
The second-place finisher neither held the Red token nor voted for Natasha. So whoever finishes second is not Red and does not cast a vote for Natasha.
The Green token holder finished exactly one place ahead of the Rope Puzzle finisher. With three places, that means Green is one place in front of Rope Puzzle.
The Blue token holder finished before the Obstacle Crawl. So Blue must be earlier than the Obstacle Crawl finisher.
The last-place finisher and the second-place finisher voted for the same person. So places two and three share a vote target.
Miles did not vote for Finn. So Miles’s target is either Miles’s other opponent (Natasha) or, if allowed, someone else consistent with no self-votes. Because self-votes are not allowed, Miles must have voted for Natasha.
The challenges finished in this order: Balance Beam, then Obstacle Crawl, then Rope Puzzle. This means Balance Beam is first, Obstacle Crawl is second, and Rope Puzzle is third.
The voter for Natasha held the Blue token, and it was not Finn. From earlier we deduced Miles voted for Natasha. Therefore Miles held the Blue token.
Natasha did not attempt the Balance Beam, and she did not hold the Red token. So Natasha’s challenge is either Obstacle Crawl or Rope Puzzle, and her token is either Blue or Green. But Blue is already Miles’s token, so Natasha must hold Green.
The Red token holder did not vote for Finn. Red’s voter is therefore not someone who targeted Finn.
Now combine the fixed challenge order with the Green-ahead-of-Rope condition. Rope Puzzle is third. Therefore the Green token holder finished exactly one place ahead of third, which is second. Since Natasha holds Green, Natasha finished second on the Obstacle Crawl. That places Miles, the Blue token holder, before the Obstacle Crawl as required, so Miles finished first on the Balance Beam. Finn is the remaining contestant and must be third on the Rope Puzzle, which also means Finn holds the remaining token, Red.
Use the voting rules. Miles already voted for Natasha. The second-place finisher and the last-place finisher voted for the same person, so Natasha (second) and Finn (third) must share a target. They cannot vote for Natasha because the second-place finisher may not vote for Natasha, and no one may vote for themselves. They cannot both vote for Finn because Finn cannot vote for himself. Therefore both Natasha and Finn must have voted for Miles. This also satisfies that the Red token holder (Finn) did not vote for Finn.
Everything is consistent: Miles is Blue and did not do the Rope Puzzle, satisfying the “exactly one” condition; Blue finishes before Obstacle Crawl; Green is one place ahead of Rope Puzzle; the second-place finisher is not Red and does not vote for Natasha; and places two and three share the same vote target.
Answers
Miles finished 1st on the Balance Beam, held the Blue token, and voted for Natasha.
Natasha finished 2nd on the Obstacle Crawl, held the Green token, and voted for Miles.
Finn finished 3rd on the Rope Puzzle, held the Red token, and voted for Miles.
Miles is eliminated.
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