Algebra Introduction 4 with Chinese Numerals, Mortensen Math China, Algebra, Factoring Expressions, with Jerry Mortensen, Mortensen Math manipulative blocks, Kids Montessori K-12 Homeschooling Pre-school Kindergarten mathematics tutorial video.\
Math, Calculus, Trigonometry, Fractions, Algebra, Addition, Subtraction, Multiplication, Factoring
Algebra visualization with Mortensen Math.com manipulative colored blocks to visualizing algebraic expressions, visualizing mathematics, Montessori Homeschool k-12 preschool online curriculum on line video.
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In this video, you will learn the basics of writing paragraphs.

We hope you are enjoying this video! For more in-depth learning, check out Miacademy.co (https://www.parents.miacademy.co/), an online learning platform with lessons and practice games that go along with our videos. Use coupon code VIDEOSPECIAL for a discount. Good for homeschoolers, Parents, Teachers, or anyone with kids in grades K-8.

Miacademy also offers many hands-on learning activities including a business simulation, writing in the Miacademy weekly, and creating artwork. Teaching social skills is also one of the key values at Miacademy. On the site, kids can interact safely in a moderated environment and share their artwork, videos, and ideas with each other.

Learn what it's like to be a lodging manager from someone working in the field!
We hope you are enjoying our large selection of engaging core & elective K-12 learning videos. New videos are added all the time - make sure you come back often to learn more! If you'd like us to cover any additional topics, please let us know. For practice, assessment, and many interactive activities that go along with each video, as well as a teacher/parent dashboard, go to Miacademy.co for Grades K-8 or Miaprep.com for grades 9-12!

Learn about the physical characteristics of Oceania and Antarctica, economic activities in Oceania, and how Antarctica is governed!
We hope you are enjoying our large selection of engaging core & elective K-12 learning videos. New videos are added all the time - make sure you come back often to learn more! If you’d like us to cover any additional topics, please let us know.
For practice, assessment, and many interactive activities that go along with each video, as well as a teacher/parent dashboard, go to Miacademy.co for Grades K-8 or Miaprep.com for grades 9-12!

Learn about the land, climate, cultural background, and economic and political structures of New Zealand!
We hope you are enjoying our large selection of engaging core & elective K-12 learning videos. New videos are added all the time - make sure you come back often to learn more! If you’d like us to cover any additional topics, please let us know.
For practice, assessment, and many interactive activities that go along with each video, as well as a teacher/parent dashboard, go to Miacademy.co for Grades K-8 or Miaprep.com for grades 9-12!

How to simplify square roots. I give step by step instructions on how to simplify a square root. Once you see a couple examples I think you will find the process pretty easy.

List Perfect Square, Cube, and Fourth Roots
http://www.moomoomathblog.com/....2020/07/perfert-squa

This organic chemistry video tutorial provides a basic introduction into reaction mechanisms. It explains the four fundamental reactions such as addition reactions, elimination reactions, substitution reactions, and rearrangements.

Here is a list of topics:
1. Electrophilic Addition Reactions of Alkenes
2. Nucleophilic Addition Reactions of Ketones
3. Carbocation Rearrangements and Ring Expansion Examples
4. SN2 SN1 E1 and E2 Reaction Mechanisms
5. Nucleophilic Substitution Reactions
6. Elimination Reactions
7. E1CB Reaction
8. Free Radical Reactions - Radical Substitution Mechanism
9. Electrophilic Aromatic Substitution Reactions
10. Nucleophilic Aromatic Substitution Reactions
11. Addition Elimination Reaction Mechanism
12. Elimination Addition Reaction Mechanism

Organic Chemistry PDF Worksheets: https://www.video-tutor.net/orgo-chem.html
Organic Chemistry Exam 1 Playlist: https://bit.ly/3kJnNXU
Organic Chemistry 1 Exam 2 Playlist: https://bit.ly/3PKEApB
List of Extended Organic Chemistry Videos: https://www.youtube.com/watch?v=7kDoqNo3sNA
________________________________________________________________________________________________
Organic Chemistry - Basic Introduction: https://www.youtube.com/watch?v=B_ketdzJtY8
How To Draw Lewis Structures: https://www.youtube.com/watch?v=6unef5Hz6SU
Functional Groups Review: https://www.youtube.com/watch?v=m9jM8lWxrAE
How To Calculate Formal Charge: https://www.youtube.com/watch?v=R_SIjijCouE
Valence Bond Theory: https://www.youtube.com/watch?v=Vqx9a2aU99c
Hybridization of Atomic Orbitals: https://www.youtube.com/watch?v=pdJeQUd2g_4
Bond Length & Bond Strength: https://www.youtube.com/watch?v=SSRY95IAwF8
Resonance Structures: https://www.youtube.com/watch?v=OqsOIp5UuME
Acids and Bases - Introduction: https://www.youtube.com/watch?v=owVZiKnnPME
pKa Values of Acids: https://www.youtube.com/watch?v=L7flgA0n_tc
Constitutional Isomers: https://www.youtube.com/watch?v=48rsf1pOhfA
IUPAC Nomenclature of Alkanes: https://www.youtube.com/watch?v=TYU_JluleME
Naming Cycloalkanes: https://www.youtube.com/watch?v=vSxZm_91GT0
Naming Bicyclic Compounds: https://www.youtube.com/watch?v=L8wEn7sD_SA
Boiling Point of Organic Compounds: https://www.youtube.com/watch?v=Qk_uPsq10TI
Newman Projections: https://www.youtube.com/watch?v=_CCHTptAhLQ
Chair Conformations: https://www.youtube.com/watch?v=RXU_32X1oFI
Organic Chemistry Exam 1 Review: https://www.youtube.com/watch?v=7ofZXNAG3AY
Organic Chemistry Exam 1 Questions: https://www.youtube.com/watch?v=YT8F6pUbLJw
Stereochemistry R/S Configuration: https://www.youtube.com/watch?v=yzfcrwJ37kI
Optical Activity & Specific Rotation: https://www.youtube.com/watch?v=duGxp_XZzvw
SN1, SN2, E1, E2 Reaction Mechanisms: https://www.youtube.com/watch?v=hz-fSXifP9w
SN2 Reaction Mechanisms: https://www.youtube.com/watch?v=k_spZVJtzFE
SN1 Reaction Mechanisms: https://www.youtube.com/watch?v=rRAKyR7hX-U
SN1, SN2, E1, E2 - Practice Test: https://www.youtube.com/watch?v=qTc2uud7TVU
Naming Alkenes - E/Z System: https://www.youtube.com/watch?v=frtnEDTSzi8
Index of Hydrogen Deficiency: https://www.youtube.com/watch?v=M7xm5CKIHEc
Alkene Reactions Review: https://www.youtube.com/watch?v=lKROX1C0JRs
Alkyne Reactions Review: https://www.youtube.com/watch?v=p6TLF92lyuI
Organic Chemistry Exam 2 Review: https://www.youtube.com/watch?v=h_6qYq3_ftA
Organic Chemistry Exam 2 Questions: https://www.youtube.com/watch?v=Lenac3a1zQM
Alcohol Reactions: https://www.youtube.com/watch?v=4PDs3ygNsv4
Free Radical Reactions: https://www.youtube.com/watch?v=w9RAULFkqKQ
Organic Chemistry Reactions Summary: https://www.youtube.com/watch?v=nkh0egRNQz0
Organic Chemistry 1 Final Exam Review: https://www.youtube.com/watch?v=ej2pSWw6U3w
Organic Chemistry 2 Final Exam Review: https://www.youtube.com/watch?v=T5NaUdVfAOc

This calculus video tutorial provides a basic introduction into derivatives for beginners. Here is a list of topics:

Derivatives - Fast Review: https://www.youtube.com/watch?v=5yfh5cf4-0w&t=1s

Limit Definition of the Derivative:
https://www.youtube.com/watch?v=-aTLjoDT1GQ

Derivatives - Alternate Limit Definition:
https://www.youtube.com/watch?v=6yzaEpacZkg

Derivatives - The Constant Rule:
https://www.youtube.com/watch?v=cyn6CDnAlcA

Derivatives - The Power Rule:
https://www.youtube.com/watch?v=9Yz-RCdS2Tg

_________________________________
Derivatives - Constant Multiple Rule:
https://www.youtube.com/watch?v=ut-AFj600S0

Derivatives - Polynomial Functions:
https://www.youtube.com/watch?v=8Sv6CNuNwqo

Derivatives - Sine and Cosine:
https://www.youtube.com/watch?v=QYJx-ztCrE4

Derivatives - Trigonometric Functions:
https://www.youtube.com/watch?v=PEqCa0U77mc

Derivatives - Limits:
https://www.youtube.com/watch?v=xGibYZiT5-U

_______________________________________
Equation of the Tangent Line:
https://www.youtube.com/watch?v=5NyeGzbBJQM

Derivatives - Horizontal Tangent Line:
https://www.youtube.com/watch?v=aNfoxbMUOHk

The Equation of The Normal Line:
https://www.youtube.com/watch?v=lEF2mmR3CWU

The Equation of The Secant Line:
https://www.youtube.com/watch?v=680o1GL-LRg

Average and Instantaneous Velocity:
https://www.youtube.com/watch?v=AwxT1xjMP9g

_______________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/

Full-Length Videos and Worksheets:
https://www.patreon.com/MathSc....ienceTutor/collectio

This video explains how to find the range of a function. Examples include quadratic functions, linear functions, absolute value functions, and square root or radical functions.

Functions and Graphs Practice Test: https://www.youtube.com/watch?v=kvU9sOzT2mk

Transformations of Functions:
https://www.youtube.com/watch?v=Tmdrjs9xufc

____________________________________________
How To Find The Range of a Function:
https://www.youtube.com/watch?v=Si2vmzUWfJE

Domain and Range - More Examples:
https://www.youtube.com/watch?v=KyOQhC8ctxc

Domain and Range From a Graph:
https://www.youtube.com/watch?v=KirGQOwjBVI

____________________________________________
Domain and Range - Radical Functions:
https://www.youtube.com/watch?v=VM3iMj0BwLE

Domain of Logarithmic Functions:
https://www.youtube.com/watch?v=WfgYJy035k0

Domain and Range - Piecewise Functions:
https://www.youtube.com/watch?v=0ZoSxPg6JSQ

Domain and Range - Inverse Functions:
https://www.youtube.com/watch?v=wP4JjdFbCkY

_____________________________________________
SAT Math Test Prep:
https://www.youtube.com/watch?v=fTGuTEQCsZY

ACT Math Test Prep:
https://www.youtube.com/watch?v=SsA7rZ8kczM

Final Exams and Video Playlists:
https://www.video-tutor.net/

Full-Length Math & Science Videos:
https://www.patreon.com/mathsc....iencetutor/collectio

This statistics video tutorial explains how to solve hypothesis testing problems with proportions. It explains how to calculate the sample proportion and the z-test statistic and how to compare that with the critical values in order to determine whether or not if you should accept or reject the null hypothesis at a specified confidence level or significance level.

Confidence Intervals & Margin of Error:
https://www.youtube.com/watch?v=DT-fPG0Hff8

Find The Z-Score Given Confidence Interval:
https://www.youtube.com/watch?v=sJyZ9vRhP7o

Student's T-Distribution:
https://www.youtube.com/watch?v=MUD390jtgQs

Hypothesis Testing - Null & Alternative:
https://www.youtube.com/watch?v=wiYJWyfdGg4

Type I and Type II Errors:
https://www.youtube.com/watch?v=9yQm9F2_yIk

One Tailed and Two Tailed Tests:
https://www.youtube.com/watch?v=XHPIEp-3yC0

_______________________________________
Test Static For Means & Pop Proportions:
https://www.youtube.com/watch?v=Hag0GW9B6EY

Hypothesis Testing Problems:
https://www.youtube.com/watch?v=zJ8e_wAWUzE

P-Value Method - Hypothesis Testing:
https://www.youtube.com/watch?v=8Aw45HN5lnA

Hypothesis Testing - Proportions:
https://www.youtube.com/watch?v=76VruarGn2Q

Difference of 2 Means - H Testing:
https://www.youtube.com/watch?v=UcZwyzwWU7o

Cohen's D - Pooled Standard Deviation:
https://www.youtube.com/watch?v=GDe4M0xEghs

Hypothesis Testing - 2 Proportions:
https://www.youtube.com/watch?v=pCbNUnZ98oE

__________________________________
Matched or Paired Samples t-Test:
https://www.youtube.com/watch?v=JiQR0lHLe74

Chi Square Test:
https://www.youtube.com/watch?v=HKDqlYSLt68

Chi Square Distribution Test:
https://www.youtube.com/watch?v=O6a76Dnn104

Test of Independence - Chi Square Dist:
https://www.youtube.com/watch?v=y5nxiL6civU

Final Exams and Video Playlists:
https://www.video-tutor.net/

Full-Length Videos and Worksheets:
https://www.patreon.com/MathSc....ienceTutor/collectio

This calculus video tutorial explains how to find the absolute maximum and minimum values of a function on a closed interval. Tto find the absolute extrema, you need to find the relative extrema by finding the first derivative of the function and the critical numbers. Plot the critical numbers on a number line to create sign chart. Using the sign chart and the first derivative test, determine what type of relative extrema is present - if it's a relative maximum or a relative minimum. Next, place the critical numbers and the endpoints of the closed interval into an x y data table and compare the y values. The absolute maximum contains highest y value and the absolute minimum has the lowest y value.

Introduction to Limits:
https://www.youtube.com/watch?v=YNstP0ESndU

Derivatives - Fast Review:
https://www.youtube.com/watch?v=5yfh5cf4-0w

Introduction to Related Rates:
https://www.youtube.com/watch?v=I9mVUo-bhM8

_____________________________
Extreme Value Theorem:
https://www.youtube.com/watch?v=Sx2lPZlnWfs

Finding Critical Numbers:
https://www.youtube.com/watch?v=Bp9EbV3COVA

Local Maximum & Minimum:
https://www.youtube.com/watch?v=WCq3sRzsJfs

Absolute Extrema:
https://www.youtube.com/watch?v=3wrXDw5ETh4

Rolle's Theorem:
https://www.youtube.com/watch?v=LHym1ARc2cE

________________________________
Mean Value Theorem:
https://www.youtube.com/watch?v=SL2RobwU_M4

Increasing and Decreasing Functions:
https://www.youtube.com/watch?v=Dyl7jPlJXOM

First Derivative Test:
https://www.youtube.com/watch?v=G5wlKltW7pM

Concavity & Inflection Points:
https://www.youtube.com/watch?v=OhqNbQi9QPk

Second Derivative Test:
https://www.youtube.com/watch?v=G8GAsYkZlpE

_________________________________
L'Hopital's Rule:
https://www.youtube.com/watch?v=Gh48aOvWcxw

Curve Sketching With Derivatives:
https://www.youtube.com/watch?v=JTVNUdL7sWs

Newton's Method:
https://www.youtube.com/watch?v=-5e2cULI3H8

Optimization Problems:
https://www.youtube.com/watch?v=lx8RcYcYVuU

_______________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/

Full-Length Videos and Worksheets:
https://www.patreon.com/MathSc....ienceTutor/collectio

This calculus video tutorial provides multiple choice practice problems on limits and continuity.

Introduction to Limits: https://www.youtube.com/watch?v=YNstP0ESndU

How To Evaluate Limits From a Graph:
https://www.youtube.com/watch?v=7Q2HwTHcxA0

Evaluating Limits By Factoring:
https://www.youtube.com/watch?v=fOrOeZA-vdY

Limits of Rational Functions :
https://www.youtube.com/watch?v=M2BgBG2Su94

Limits of Radical Functions:
https://www.youtube.com/watch?v=qay5HvT1UK8

Limits of Trigonometric Functions:
https://www.youtube.com/watch?v=HbtuSC_WOW0

___________________________________
How To Find The Limit at Infinity:
https://www.youtube.com/watch?v=NmLljBAg82o

Infinite Limits + Vertical Asymptotes:
https://www.youtube.com/watch?v=xvFqomOpLrs

Limits at Infinity With Radicals:
https://www.youtube.com/watch?v=1hyoTeWg6Bs

Limits of Absolute Value Functions:
https://www.youtube.com/watch?v=wFeh4ByT0xs

Limits of Composite Functions:
https://www.youtube.com/watch?v=KjL9cWHzeIc

The Squeeze Theorem:
https://www.youtube.com/watch?v=lVIb9iJ-rRI

____________________________________
Limits and Logarithms:
https://www.youtube.com/watch?v=fHzmQmcvheI

Limits of Exponential Functions:
https://www.youtube.com/watch?v=pcUXo7XbRaM

Piecewise Functions - Limits:
https://www.youtube.com/watch?v=JrYmEo6hoiU

3 Step Continuity Test:
https://www.youtube.com/watch?v=WT7oxiiFYt8

Continuity and Differentiability:
https://www.youtube.com/watch?v=fml0-ELYLaE

Limits - Test Review:
https://www.youtube.com/watch?v=6e4Wtgc43KQ

_____________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/

Full-Length Videos and Worksheets:
https://www.patreon.com/MathSc....ienceTutor/collectio

Creating scaling and reflection transformation matrices (which are diagonal)

Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/linear-transformation-examples-rotations-in-r2?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/linear_transformations/v/more-on-matrix-addition-and-scalar-multiplication?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channe....l/UCGYSKl6e3HM0PP7QR
Subscribe to KhanAcademy: https://www.youtube.com/subscr....iption_center?add_us

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/ap-statistics/den

Discussion of how "normal" a distribution might be

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/probability/statistics-inferential/normal_distribution/e/empirical_rule?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Watch the next lesson: https://www.khanacademy.org/math/probability/statistics-inferential/normal_distribution/v/ck12-org-normal-distribution-problems-empirical-rule?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Missed the previous lesson?
https://www.khanacademy.org/math/probability/statistics-inferential/normal_distribution/v/normal-distribution-excel-exercise?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics

Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Probability and Statistics channel:
https://www.youtube.com/channe....l/UCRXuOXLW3LcQLWvxb
Subscribe to KhanAcademy: https://www.youtube.com/subscr....iption_center?add_us

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Title Vlog: Making Meaning Through Language (Component 3) English Curriculum

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We at Swami Vivekanand Public School Huda sec 17 are working hard to keep the flow of learning going. Your kind feedbacks will help us do even better. Please Suggest us ways to make this #schoolfromhome a better experience for you and the kids.

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Learn about Davy Crockett in this biography for kids! Kids will learn all about Davy Crockett and his times. Learn why he was one of the most influential men of his time, and how he became the stuff of legend long after his death.
Homeschool Pop offers a unique, dynamic learning experience. We strive to have the right balance of silliness and learning to keep students engaged as we look at the life of Davy Crockett in this biography.

We hope you enjoyed the classroom edition of the Davy Crockett video! Thanks for watching, and we hope you will keep watching and learning. You are awesome!


Davy Crockett Biography For Kids | Classroom Edition

Deep beneath Antarctica’s icy surface, scientists have uncovered something straight out of prehistory — an ancient egg dating back 66 million years. But that’s only the beginning. In this video, we’ll dive into the ocean’s strangest secrets: creatures that lived alongside the dinosaurs, bizarre life forms still thriving in the deep today, and new discoveries that keep rewriting the history of Earth’s seas. From prehistoric predators to mysterious ocean dwellers, get ready for a journey that’s as chilling as it is fascinating.
Animation is created by Bright Side.
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Check our Bright Side podcast on Spotify and leave a positive review! https://open.spotify.com/show/....0hUkPxD34jRLrMrJux4V
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This video is made for entertainment purposes. We do not make any warranties about the completeness, safety and reliability. Any action you take upon the information in this video is strictly at your own risk, and we will not be liable for any damages or losses. It is the viewer's responsibility to use judgement, care and precaution if you plan to replicate.

The 100 Prisoners Riddle feels completely impossible even once you know the answer. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription.

Special thanks to Destin of Smarter Every Day (https://ve42.co/SED), Toby of Tibees (https://ve42.co/Tibees), and Jabril of Jabrils (https://ve42.co/Jabrils) for taking the time to think about this mind bending riddle.

Huge thanks to Luke West for building plots and for his help with the math.
Huge thanks to Dr. Eugene Curtin and Dr. Max Warshauer for their great article on the problem and taking the time to help us understand it: https://ve42.co/CurtinWarshauer
Thanks to Dr. John Baez for his help with finding alternate ways to do the calculations.
Thanks to Simon Pampena for his input and analysis.

Other 100 Prisoners Riddle videos:
minutephysics: https://www.youtube.com/watch?v=C5-I0bAuEUE
Vsauce2: https://www.youtube.com/watch?v=kOnEEeHZp94
Stand-up Maths: https://www.youtube.com/watch?v=a1DUUnhk3uE
TED-Ed: https://www.youtube.com/watch?v=vIdStMTgNl0

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References:
Original paper: Gál, A., & Miltersen, P.B. (2003). The Cell Probe Complexity of Succinct Data Structures. BRICS, Department of Computer Science, University of Aarhus. All rights reserved. – https://ve42.co/GalMiltersen
Winkler, P. (2006). Seven Puzzles You Think You Must Not Have Heard Correctly. – https://ve42.co/Winkler2006
The 100 Prisoners Problem – https://ve42.co/100PWiki
Golomb, S. & Gaal, P. (1998). On the Number of Permutations on n Objects with Greatest Cycle Length k. Advances in Applied Mathematics, 20(1), 98-107. – https://ve42.co/Golomb1998
Lamb, E. (2012). Puzzling Prisoners Presented to Promote North America's Only Museum of Math. Observations, Scientific American. – https://ve42.co/Lamb2012
Permutations – https://ve42.co/PermutationsWiki
Probability that a random permutation of n elements has a cycle of length k greater than n/2, Math SE. – https://ve42.co/BaezProbSE
Counting Cycle Structures in Sn, Math SE. – https://ve42.co/CountCyclesSE
What is the distribution of cycle lengths in derangements? In particular, expected longest cycle, Math SE. – https://ve42.co/JorikiSE
The Manim Community Developers. (2021). Manim - Mathematical Animation Framework (Version v0.13.1). – https://www.manim.community/

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Special thanks to Patreon supporters: RayJ Johnson, Brian Busbee, Jerome Barakos M.D., Amadeo Bee, Julian Lee, Inconcision, TTST, Balkrishna Heroor, Chris LaClair, Avi Yashchin, John H. Austin, Jr., OnlineBookClub.org, Matthew Gonzalez, Eric Sexton, john kiehl, Diffbot, Gnare, Dave Kircher, Burt Humburg, Blake Byers, Dumky, Evgeny Skvortsov, Meekay, Bill Linder, Paul Peijzel, Josh Hibschman, Timothy O’Brien, Mac Malkawi, Michael Schneider, jim buckmaster, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Stephen Wilcox, Marinus Kuivenhoven, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

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Written by Derek Muller and Emily Zhang
Filmed by Derek Muller and Petr Lebedev
Animation by Ivy Tello and Jesús Rascón
Edited by Trenton Oliver
Additional video/photos supplied by Getty Images
Music from Epidemic Sound and Jonny Hyman
Thumbnail by Ignat Berbeci
Produced by Derek Muller, Petr Lebedev, and Emily Zhang