Puzzle 20: The Uneven Tower of Stones

Puzzle Walkthrough

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The tower that collapsed three times was shorter than Natasha’s and was not built on the Flat base. So the three-collapse tower is on either Rounded, Slanted, or Jagged, and its height is below Natasha’s.

Exactly one of the two middle heights, 6′6″ or 6′10″, stood on a Flat base. So Flat carries either 6′6″ or 6′10″, and the Flat tower has whichever of those heights we later confirm.

Dante’s tower was taller than Natasha’s, and it collapsed more often than the tower on the Jagged base. That means the Jagged tower has fewer collapses than Dante, and Dante’s height is above Natasha’s.

The Slanted base was used by a contestant whose tower was taller than every tower that collapsed zero or one times. So the Slanted tower’s height must exceed both the zero-collapse tower and the one-collapse tower.

Cassidy’s tower did not use the Rounded base, and it stood exactly four inches taller than Natasha’s. Since the heights are spaced in four-inch steps (6′2″, 6′6″, 6′10″, 7′2″), Cassidy’s height is exactly one step above Natasha’s.

Among the Flat and Rounded bases, one had zero collapses and the other had three collapses. So Flat and Rounded take the collapse counts 0 and 3 in some order.

Axel’s tower was not built on the Flat base and was not the tallest. So Axel cannot be Flat, and Axel’s height is not 7′2″.

The tallest tower did not use the Rounded base. So 7′2″ is on either Flat, Slanted, or Jagged, but not Rounded.

Exactly one tower with two collapses was taller than Cassidy’s. Since collapse counts are all distinct, the unique two-collapse tower stands higher than Cassidy.

The tower on the Jagged base did not match the shortest height. So Jagged is not 6′2″.

Cassidy’s tower collapsed fewer times than Natasha’s. So Cassidy’s collapse count is less than Natasha’s.

Now pin down the global structure. From “Flat and Rounded are 0 and 3 collapses” and “the three-collapse tower is not Flat,” Flat must be the zero-collapse base and Rounded must be the three-collapse base. The three-collapse tower is shorter than Natasha’s, so Natasha cannot be the three-collapse tower. Also, the tallest tower is not Rounded, which is already consistent.

Use the comparison chain. Cassidy is exactly one height step above Natasha, and Dante is taller than Natasha. To make the two-collapse tower taller than Cassidy (and thus satisfy the “exactly one tower with two collapses was taller than Cassidy’s”), the natural fit is:
Natasha at 6′6″,
Cassidy at 6′10″,
Dante at 7′2″,
leaving Axel at 6′2″.
This ordering makes Dante (who we will soon see has two collapses) taller than Cassidy as required, and leaves a height lower than Natasha for the three-collapse tower.

Now resolve bases and collapses. Rounded carries three collapses and must be shorter than Natasha; that matches Axel at 6′2″, and Axel is not Flat and not the tallest, which fits perfectly. Jagged has fewer collapses than Dante’s and cannot be the shortest height; so Jagged must be the one-collapse tower at a height above 6′2″. That forces Dante to have two collapses, since three collapses are already Rounded and one collapse is Jagged. With Dante at 7′2″ and two collapses, the Slanted condition is automatically satisfied if Dante’s base is Slanted: his tower is taller than every tower with zero or one collapses. Therefore assign Slanted to Dante.

Flat is the zero-collapse base and must carry one of the middle heights. With Axel already on Rounded and Dante on Slanted, Flat must go to either Cassidy or Natasha. Cassidy’s collapses are fewer than Natasha’s, so give Flat’s zero collapses to Cassidy and the Jagged base with one collapse to Natasha. That also satisfies the Jagged rule about not being the shortest height.

Every clue now checks:
the three-collapse tower (Rounded) is shorter than Natasha and not Flat,
Flat is zero collapses,
Dante is taller than Natasha and has more collapses than Jagged,
Slanted’s tower (Dante) is taller than all zero- and one-collapse towers,
Cassidy is one step taller than Natasha and not Rounded,
Flat and Rounded are 0 and 3,
Axel is not Flat and not tallest,
the tallest is not Rounded,
the two-collapse tower (Dante) is taller than Cassidy,
Jagged is not the shortest height,
and Cassidy’s collapses are fewer than Natasha’s.

Answers

Dante built on the Slanted base, his tower was 7′2″, and it collapsed 2 times.
Cassidy built on the Flat base, her tower was 6′10″, and it collapsed 0 times.
Axel built on the Rounded base, his tower was 6′2″, and it collapsed 3 times.
Natasha built on the Jagged base, her tower was 6′6″, and it collapsed 1 time.

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