Puzzle 17: The Signal Fire

Puzzle Walkthrough

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The fire built with Thick Branches was taller than every other fire, and it was neither the first nor the last to ignite. That makes the Thick Branches fire the tallest at 9’3”, and its time must be either 4:08 or 5:21.

The 8’0” flame was lit immediately after the Driftwood fire. So the Driftwood fire’s time is one slot earlier than the 8’0” flame’s time.

Natasha’s flame was taller than exactly one other flame. Among the four heights, only 7’1” is taller than exactly one other (it is taller than 6’4” and shorter than 8’0” and 9’3”). Therefore Natasha’s height is 7’1”.

Cassidy lit her fire before Dante. So Cassidy’s time is earlier than Dante’s.

Jessica did not use Palm Fronds. Keep that in mind for later placements.

The Vines & Twigs fire measured neither 7’1” nor 8’0”. The tallest height 9’3” already belongs to Thick Branches, so Vines & Twigs must be 6’4”.

The Palm Fronds fire ignited before the Thick Branches fire. So the Palm Fronds time is earlier than the Thick Branches time.

Cassidy did not use Driftwood. So Cassidy cannot be the person whose fire comes immediately before the 8’0” flame.

The 6’4” fire took longer to ignite than Dante’s fire. Since 6’4” is the Vines & Twigs fire, whoever used Vines & Twigs lit theirs later than Dante.

Exactly one contestant’s fire was lit between Natasha and Dante. So their times are separated by exactly one position.

Now thread these together. Natasha is 7’1”. The 8’0” flame must come immediately after Driftwood. Because Cassidy cannot be Driftwood, the only way to satisfy “one between Natasha and Dante” along with “Cassidy before Dante” and “Vines & Twigs later than Dante” is this timing: Natasha at 3:12, Cassidy at 4:08, Dante at 5:21, and the remaining time 6:45 for the last contestant. This arrangement places exactly one person between Natasha and Dante, keeps Cassidy earlier than Dante, and allows the Vines & Twigs fire to be later than Dante.

Place the Driftwood and the 8’0” pair. With Natasha at 3:12 and Cassidy at 4:08, the immediate-after rule fits perfectly if Natasha used Driftwood and Cassidy’s height was 8’0”. That also respects Cassidy not using Driftwood.

Now place the tallest and the remaining woods. The tallest 9’3” height belongs to Thick Branches, and it cannot be first or last to ignite. In our timeline, the middle times are 4:08 and 5:21; 4:08 is Cassidy (already 8’0”), so the 9’3” Thick Branches must be Dante at 5:21. That automatically satisfies “Palm Fronds ignited before Thick Branches,” so assign Palm Fronds to Cassidy at 4:08.

Vines & Twigs is 6’4” and must be later than Dante. The only time later than 5:21 is 6:45, so Jessica must be Vines & Twigs at 6:45. That leaves Natasha as Driftwood at 3:12, which we already used to satisfy the 8’0” immediately-after rule.

Answers

Dante used Thick Branches, lit at 5:21, and his flame was 9’3”.
Cassidy used Palm Fronds, lit at 4:08, and her flame was 8’0”.
Jessica used Vines & Twigs, lit at 6:45, and her flame was 6’4”.
Natasha used Driftwood, lit at 3:12, and her flame was 7’1”.

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