MIT Mystery Hunt 2020/Torsion Twirl: Difference between revisions

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|author =
|author = Shelly Manber
|answer =
|answer = THE TWIST
|solves =
|solves = 22
|guesses = <!-- total (correct and incorrect) -->
|guesses = 53
|link = <!-- puzzle link, these should all be plain URLs -->
|link = https://puzzles.mit.edu/2020/puzzle/torsion_twirl/
|solution_link =
|solution_link = https://puzzles.mit.edu/2020/puzzle/torsion_twirl/solution/
|checker_link =
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'''Torsion Twirl''' is a [INSERT PUZZLE TYPE] puzzle from the {{l|Yesterdayland}} round of the [[MIT Mystery Hunt 2020|2020 MIT Mystery Hunt]]. It [INSERT BRIEF DESCRIPTION]
'''Torsion Twirl''' is a puzzle from the {{l|Yesterdayland}} round of the [[MIT Mystery Hunt 2020|2020 MIT Mystery Hunt]].


==Solve Path==
[[Category:Pages without solve path]]

[[Category: Pages that need images]]
==Puzzle Elements==
==Puzzle Elements==


{{Element|Flavortext|''I really enjoyed riding the torsion twirl, but I got so dizzy… These dancers curve effortlessly! They told me the trick is they always get back exactly where they started in finitely many steps, they just have to make sure they know how many. “It’s all about the order,” they said.''}}
* [INSERT ELEMENTS]

{{Element|Video|The puzzle is presented as eight short videos of two dancers turning. One dancer is marked with an X and the other with a Y.}}

{{spoiler|label=Spoiler-y Elements}}

{{Element|Hint in Title|The "torsion" in Torsion Twirl refers to [https://en.wikipedia.org/wiki/Torsion_subgroup torsion points] on elliptic curves.}}

{{Element|Hint in Flavortext|''I really enjoyed riding the torsion twirl, but I got so dizzy… These dancers [https://en.wikipedia.org/wiki/Elliptic_curve curve] effortlessly! They told me the trick is they [https://en.wikipedia.org/wiki/Torsion_subgroup always get back exactly where they started in finitely many steps], they just have to '''make sure they know how many'''. “It’s all about the [https://en.wikipedia.org/wiki/Order_(group_theory) order],” they said.''}}

{{Element|Dance|The dancers in each video perform a different kind of [https://en.wikipedia.org/wiki/Turn_(dance_and_gymnastics) turn] some number of times; the turn can be identified, using the [[enumeration]] below each video as a guideline.|Identification||Performing Arts - Dance}}

{{Element|Mathematics|At the bottom are a number of equations for [https://en.wikipedia.org/wiki/Elliptic_curve elliptic curves]. Each video's dancers turns some finite integer number of times; they are labeled with X and Y, thus uniquely identifying a point on the plane. Each point lies on exactly one of the elliptic curves in question, which allows a [[Pairs and Groups|bijection]] between the two. The solver then needs to find the order of this point according to the [https://en.wikipedia.org/wiki/Elliptic_curve#The_group_law elliptic curve group law]. This can be determined manually by drawing tangent lines to the curve, but the puzzle recommends using [https://pari.math.u-bordeaux.fr/ PARI/GP] to help with the calculations.

{{To do}} Example|Knowledge Required||Mathematics - Abstract algebra}}

{{Element|Indexing|The order of the point on that curve can then be indexed into the turn used in its video. Ordering the resulting letters using the video numbers reveals the answer.}}

{{spoiler-end}}

Latest revision as of 09:22, 13 March 2023

Torsion Twirl
MIT Mystery Hunt 2020
Yesterdayland
Author(s)Shelly Manber
AnswerClick to revealTHE TWIST
Statistics
No. solves22
No. total guesses53
Links
PuzzleLink
SolutionLink

Torsion Twirl is a puzzle from the Yesterdayland round of the 2020 MIT Mystery Hunt.

Puzzle Elements[edit | edit source]

Flavortext - I really enjoyed riding the torsion twirl, but I got so dizzy… These dancers curve effortlessly! They told me the trick is they always get back exactly where they started in finitely many steps, they just have to make sure they know how many. “It’s all about the order,” they said.

Video - The puzzle is presented as eight short videos of two dancers turning. One dancer is marked with an X and the other with a Y.

 

Hint in Title - The "torsion" in Torsion Twirl refers to torsion points on elliptic curves.

Hint in Flavortext - I really enjoyed riding the torsion twirl, but I got so dizzy… These dancers curve effortlessly! They told me the trick is they always get back exactly where they started in finitely many steps, they just have to make sure they know how many. “It’s all about the order,” they said.

Identification (Performing Arts - Dance) - The dancers in each video perform a different kind of turn some number of times; the turn can be identified, using the enumeration below each video as a guideline.

Knowledge Required (Mathematics - Abstract algebra) - At the bottom are a number of equations for elliptic curves. Each video's dancers turns some finite integer number of times; they are labeled with X and Y, thus uniquely identifying a point on the plane. Each point lies on exactly one of the elliptic curves in question, which allows a bijection between the two. The solver then needs to find the order of this point according to the elliptic curve group law. This can be determined manually by drawing tangent lines to the curve, but the puzzle recommends using PARI/GP to help with the calculations.

To do TO DO Example

Indexing - The order of the point on that curve can then be indexed into the turn used in its video. Ordering the resulting letters using the video numbers reveals the answer.

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