Puzzle 39: The Fire Circle of Logic - Web of Votes

Puzzle Walkthrough

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Start from the hard anchors. The person arriving at 8:10 PM voted first and used Future Risk. The Revenge voter arrived earliest at 8:00. Cassidy voted immediately before Harper, and Harper arrived five minutes after Cassidy, so their arrivals are consecutive with Cassidy earlier and their vote orders back-to-back with Cassidy just before Harper. Suri voted last with Alliance Pressure, and arrived later than Harper but earlier than Natasha. Also, the fourth voter voted for Finn and arrived exactly ten minutes before Suri.

Put the timing chain in place. If the fourth voter arrives ten minutes before Suri, the only valid pair is Harper at 8:05 and Suri at 8:15. That makes Harper the fourth voter and locks Cassidy to 8:00 and third in the order (immediately before Harper), satisfying both the five-minute arrival gap and “Cassidy immediately before Harper.” With Suri last (fifth), the remaining vote orders 1 and 2 must be the two remaining contestants (Finn and Natasha), and one must come immediately before the other. The clue “the 8:10 arrival is the first voter with Future Risk” therefore pins Finn to 8:10 and first with Future Risk, and forces Natasha to second. Another clue requires Natasha to have Strategic Threat, to vote before Harper (true at second), and to arrive after Harper—so Natasha must be the latest at 8:20.

Use the “latest arrival” and “earliest target” rules. The latest arrival voted for Cassidy, so Natasha’s second-order ballot targets Cassidy. The first voter also had to vote against the earliest arrival; the earliest arrival is Cassidy at 8:00, so Finn (first) also votes for Cassidy. We still need exactly three votes against the earliest arrival, and the only remaining voter who could add that third is Suri (fifth), so Suri also votes for Cassidy. The fourth-order rule says the fourth voter voted for Finn; Harper is fourth, so Harper votes for Finn. Finally, the clue “one contestant who arrived before Harper voted for the same person as Harper” points to Cassidy (the only arrival before Harper), so Cassidy must also vote for Finn. That completes the vote targets with three against Cassidy and two against Finn, matching every constraint.

All remaining reason constraints slot neatly: Suri is Alliance Pressure (given), Harper cannot be Strategic Threat or Revenge (both already used) and must not be last or first for Weakest Link, so Harper is Weakest Link; Cassidy, at the earliest arrival, is Revenge; Finn is Future Risk; and Natasha is Strategic Threat. Every arrival, order, target, and reason now cross-checks with the clues.

Answers

Cassidy arrived at 8:00 PM, voted 3rd, cited Revenge, and voted for Finn.
Harper arrived at 8:05 PM, voted 4th, cited Weakest Link, and voted for Finn.
Finn arrived at 8:10 PM, voted 1st, cited Future Risk, and voted for Cassidy.
Suri arrived at 8:15 PM, voted 5th, cited Alliance Pressure, and voted for Cassidy.
Natasha arrived at 8:20 PM, voted 2nd, cited Strategic Threat, and voted for Cassidy.

Cassidy is eliminated.

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