Puzzle 45: Betrayal at the Fire Circle

Puzzle Walkthrough

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Start with the hard anchors. Jane arrived first, and Finn took the shortest time to vote (1 minute) and felt Angry. Two different people voted for Finn, and those two arrivals were neither first nor last and not consecutive—so the only possible arrival spots for the two Finn-voters are 2nd and 4th. The 7-minute voter wrote Finn, so one of those two (2nd or 4th) is the 7-minute ballot. The 4th arrival “took longer than everyone who arrived before,” so that 4th spot must exceed all earlier times; the only way to guarantee that is to put the longest time there. Suri is the Determined voter and the Determined voter took the longest time, so Suri sits 4th with 10 minutes and (as one of the two Finn-voters) votes for Finn. That leaves the other Finn-vote at 2nd, which we’ll soon assign to Dante.

Now place the 5-minute and Relieved spacing. Exactly one contestant arrived between the Relieved voter and the 5-minute voter. If we put the 5-minute ballot at 1st, Relieved must be 3rd (they’re two places apart), which neatly lets us order the required emotion chain: Nervous before Calm before Relieved. Make Jane (1st) the Nervous 5-minute voter; then put Calm at 2nd and Relieved at 3rd. (This also fits two more rules: the Nervous voter didn’t vote for Finn, and the Determined voter didn’t vote the same person as the Nervous voter.)

Next, set targets and timings around those placements. Jane is fixed to vote for Dante. The two Finn-voters are at 2nd and 4th, so the 2nd arrival votes Finn. The rule “the 5-minute voter and the 3rd arrival voted for the same target” ties the 3rd arrival to Jane’s 5-minute target—Dante. Also, “the first and last arrivals voted for the same person,” so whoever arrives last must also vote for Dante. Finally, the 3-minute voter had to arrive after the contestant they voted for; giving 3 minutes to the 3rd arrival (who votes for Dante) forces Dante to have arrived earlier than 3rd, which fits perfectly if Dante arrives 2nd.

That simultaneously makes the 2nd arrival the 7-minute Finn-vote (satisfying “the 7-minute voter wrote Finn”), and keeps the 4th arrival (Suri) as the other Finn-vote at the longest time. The only seat left for Finn himself is last (5th), which puts his 1-minute Angry ballot at 5th—and he, like Jane, votes for Dante. Every other constraint now clicks: the 4th arrival’s time (10) is longer than all earlier times (5, 7, 3); the Calm voter (2nd) arrives after Nervous (1st) and before Relieved (3rd); the second arrival and the Relieved voter cast votes for different people (Finn vs. Dante); and the 3-minute voter (3rd) arrived after the person they voted for (Dante at 2nd).

Answers

Jane arrived 1st, took 5 minutes, felt Nervous, and voted for Dante.
Dante arrived 2nd, took 7 minutes, felt Calm, and voted for Finn.
Mina arrived 3rd, took 3 minutes, felt Relieved, and voted for Dante.
Suri arrived 4th, took 10 minutes, felt Determined, and voted for Finn.
Finn arrived 5th, took 1 minute, felt Angry, and voted for Dante.

Dante is eliminated.

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