Math

People often choose the dealer in poker by “dealing to the first ace.” Is this a mathematically fair system? It is not! The video illustrates how the system favors early people being dealt cards. Calculating the theoretical expected values: http://mindyourdecisions.com/blog/2010/10/26/choosing-the-dealer-in-poker-is-dealing-to-the-first-ace-a-fair-system/ If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions Connect on social

Thanks to Francisco from Portugal for the suggestion! They say Euler asked this tricky algebra problem to his students. Reference Euler’s Riddle Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for

What is the fewest number of moves which can solve any Rubik’s Cube? It’s God’s Number. More links & stuff in full description below ↓↓↓ See our full series of Rubik’s Cube videos at: http://www.youtube.com/playlist?list=PLt5AfwLFPxWJNAdHv8TUCOmj7iKqyHZeg This video features Matt Parker, James Grime and Katie Steckles. More about Matt’s record attempt and those solving helpers at

If you ever need to practically convert temperature from weather reports, this is a neat little trick. Just memorize a few values and you can easily convert. I saw this trick in a Lifehacker article. #shorts References https://lifehacker.com/how-to-convert-celsius-to-fahrenheit-without-doing-any-1848777530 https://en.wikipedia.org/wiki/Fahrenheit#/media/File:Thermometer_CF.svg Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not

Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ This video features Dr James Grime – http://singingbanana.com Catch James in a recent Objectivity video with Brady: https://youtu.be/B4gzt8v401Q More James Grime videos on Numberphile: http://bit.ly/grimevideos More videos on Perfect Numbers: http://bit.ly/PerfectNumbers Triperfect T-Shirt… US:

Thanks to Devan from Lilin Bangsa Intercultural School for suggesting this problem! What is the radius of the small circle in between the blue circle (radius 4) and green circle (radius 2)? This was a challenge problem for students aged 14 to 15. Thanks to all patrons! Special thanks to: Shrihari Puranik Kyle Professor X

Tadashi Tokieda is back, this time with Moiré Patterns. More with Tadashi: http://bit.ly/tadashi_vids More links & stuff in full description below ↓↓↓ Out thanks also to our Patreon supporters, especially: Jeff Straathof Ken Baron Today I Found Out Roman Urbanovski Joanna & Mehdi Christian Cooper Peggy Y John Buchan Bill Shillito Andrzej ‘Yester’ Fiedukowicz Ripta

I’m sorry the clip from the show has been blocked. For more on game theory in Breaking Bad, see my post: Game Theory in Breaking Bad If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions Connect on social media. I update each site when I have a new video or blog post,

Previous video sets this up: https://youtu.be/-ruC5A9EzzE Extra on concatenation: https://youtu.be/LgnoYsbI7Uc More links & stuff in full description below ↓↓↓ We appreciate any help on Patreon – it lets us make a few more and better videos: http://www.patreon.com/numberphile Matt Parker on Numberphile playlist: http://bit.ly/Matt_Videos Matt’s channel: http://bit.ly/StandUpMaths Parker Square T-Shirt: http://bit.ly/ParkerSquareTshirt Inder J. Taneja papers… Single

What is 17 x 11? What about 15342 x 11? You can multiply numbers by 11 in your head with the trick shown in this video. If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions Connect on social media. I update each site when I have a new video or blog post,

This inequality is famous in math competitions and in theoretical proofs. But why is it true? The video presents a great geometric visualization and proof for two variables. Pay attention–I’ll use this inequality in an upcoming video! Desmos.com link https://www.desmos.com/calculator/6kbruja3wb Link to proofs of generalized case https://artofproblemsolving.com/wiki/index.php?title=Root-Mean_Square-Arithmetic_Mean-Geometric_Mean-Harmonic_mean_Inequality Playlist to watch all videos on MindYourDecisions This

Move exactly 3 matchsticks to make the two sides equal. Source https://matchstickpuzzles.blogspot.com/2021/05/631-mathematical-4-plus-0-is-not-0.html Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I

I didn’t solve this problem myself, but I felt better when I learned WolframAlpha couldn’t solve it either! But there is a way to solve it using careful mathematical reasoning. Thanks to Luka Khizambareli from Georgia for suggesting this and sending its solution! (*And you have to be really careful–I thank Aniket Gupta and Ryan

Partitions are a major part of the Ramanujan story (as shown in the new film about his life) – but what are they? More links & stuff in full description below ↓↓↓ Dr James Grime tackles the issue. Extra footage: https://youtu.be/ksHqQW94KlE More James Grime on Numberphile: http://bit.ly/grimevideos Young Tableau: https://youtu.be/vgZhrEs4tuk Shuffling: https://youtu.be/AxJubaijQbI James discusses Good

The secret to pizza’s name origin is mathematics, or so the legend goes… #Shorts Images https://commons.wikimedia.org/wiki/File:Pizza_Tikka.JPG#filelinks https://commons.wikimedia.org/wiki/File:Volume_of_a_pizza.svg Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you buy from the links below I may receive a commission for sales. (As

Thanks to Nikhil Patro for suggesting this problem! What is the sum of the corner angles in a regular 5-sided star? What if the star is not regular, what is the sum of corner angles then? There are some neat ways to solve this. I present my favorite methods. Thanks to all patrons! Special thanks

This equation has a secret meaning. #shorts Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you buy from the links below I may receive a commission for sales. (As an Amazon Associate I earn from qualifying purchases.) This has

This is one of the harder calculus problems I’ve come across. Thanks to Nguyen Huynh Khoi from Vietnam for the suggestion! Solution from https://khoahoc.vietjack.com/question/84520/cho-ham-so-f-x-co-dao-ham-va-lien-tuc-tren-doan-4-8 Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you purchase through these links, I may

We’re exploring the world of Chicken Nuggets and Frobenius numbers. 43 has long been a special number in the world of McNugget mathematics, but 11 is also important! More links & stuff in full description below ↓↓↓ This video features Dr James Grime – https://twitter.com/jamesgrime NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile

Thanks to http://www.audible.com/numberphile More links & stuff in full description below ↓↓↓ Here’s the paper Dr Grime discusses: http://arxiv.org/pdf/1101.4470.pdf OEIS: http://oeis.org Dr Grime: http://singingbanana.com 1729: http://youtu.be/LzjaDKVC4iY NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Brady’s videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady’s latest videos across all channels: http://www.bradyharanblog.com/

There’s an incredible method to calculate the square root of a perfect square in your head. MIT Entrace Exam Arithmetic 1876 WayBackMachine: https://web.archive.org/web/20190404065722/https://libraries.mit.edu/archives/exhibits/exam-entrance1876/arithmetic1876.html Square root method Burning Math http://burningmath.blogspot.com/2013/09/extracting-square-roots-mentally-at.html Square root method proof Math StackExchange https://math.stackexchange.com/questions/2069192/why-does-this-method-for-finding-the-square-root-of-a-number-work Square root method Grey Matters http://gmmentalgym.blogspot.com/2010/10/root-extractions.html#rtsqr Hindu-Arabic numeral system https://en.wikipedia.org/wiki/Hindu%E2%80%93Arabic_numeral_system Laplace quote https://en.wikipedia.org/wiki/History_of_the_Hindu%E2%80%93Arabic_numeral_system#Impact_on_arithmetic Laplace picture https://en.wikipedia.org/wiki/File:Laplace,_Pierre-Simon,_marquis_de.jpg Abacus picture https://en.wikipedia.org/wiki/Abacus#/media/File:Houghton_Typ_520.03.736_-_Margarita_philosophica.jpg

Thanks to Matej for suggesting this problem! This is from a math competition for 14 year olds in Croatia. While the problem is challenging, “you should be able to solve it” using elementary geometry and algebra. Can you figure it out? Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g This is the only

In the past 5 months, all of Mark Rober’s videos have been #1 trending on YouTube. He put his success in perspective by analogy to a statistical experiment of flipping coins. Some people pointed out the calculation wasn’t quite correct, so I thought it would be a great topic for a video. Mark Rober tweet

In 1880, James Garfield contributed a new proof of geometry’s most famous right triangle theorem. Mathematical treasure: Garfield’s proof https://www.maa.org/press/periodicals/convergence/mathematical-treasure-james-a-garfields-proof-of-the-pythagorean-theorem Engraved portrait https://en.wikipedia.org/wiki/File:GARFIELD,_James_A-President_(BEP_engraved_portrait).jpg Gizmodo post https://gizmodo.com/james-garfield-was-the-only-u-s-president-to-prove-a-m-1037750658 Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you purchase through these links,

This is a standard question to prepare for India’s famously challenging JEE Advanced exam. Here is one way to solve the question quickly. Thanks to Avinash for the suggestion! Special thanks this month to: Daniel Lewis, Robert Zarnke, Kyle, Mike Robertson. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Problem credit to David Altizio (section 3

Why five-sided figures pose a problem from Professor John Hunton – and a bit about the importance of Penrose Tiling. More links & stuff in full description below ↓↓↓ Professor Hunton works at the University of Leicester. NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile

Thanks to Juanci for the suggestion! Also thanks to everyone who shared a solution on Twitter. A special thanks to LuisAndrRomero2 who provided the first detailed solution. Special thanks this month to: Michael Anvari, Kyle. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Who can solve this one? I'm working on a video for it and

The Big Bang Theory TV is now part of math history: there’s a theorem named after Sheldon. Sources Siouxland News article https://siouxlandnews.com/news/local/morningside-college-professors-math-appearing-in-the-big-bang-theory 73 is the best number – Big Bang Theory clip Proof of the Sheldon conjecture https://math.dartmouth.edu/~carlp/sheldon02132019.pdf 73 is the best number (other properties) Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g

A tetrahedron and a pyramid have edges of equal length. If they are glued together on a triangular face with the vertices aligned, how many faces will the new shape have? This question is trickier than it looks! It stumped the test-makers. Playable demonstration: Steve Phelps has made a Geogebra worksheet that you can try

Can you solve this problem that stumped many advanced math students? References https://io9.gizmodo.com/ready-this-simple-puzzle-once-stumped-96-of-americas-1698814691 https://www.theguardian.com/science/2017/jun/05/did-you-solve-it-are-you-in-the-smartest-10-per-cent https://www.mapleprimes.com/posts/206713-Puzzle-Or-A-Simple-Exercise http://puzzles.nigelcoldwell.co.uk/seventytwo.htm https://timss.bc.edu/timss1995i/TIMSSPDF/C_full.pdf Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube

There are 25 mechanical horses and a single racetrack. Each horse completes the track in a pre-programmed time, and the horses all have different finishing times, unknown to you. You can race 5 horses at a time. After a race is over, you get a printout with the order the horses finished, but not the

Colin Rizzio became famous after finding a mistake on the S.A.T. Sources https://www.deseret.com/1997/2/7/19293720/math-question-on-the-sat-didn-t-sit-well https://people.com/archive/flunking-the-tester-vol-47-no-7/ https://www.chicagotribune.com/news/ct-xpm-1997-02-07-9702070268-story.html https://www.dartmouth.edu/~chance/chance_news/recent_news/chance_news_6.03.html Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to

Thanks to Dhrubajyoti for the suggestion! A similar problem was asked to class 10 students in India (Q33 from SMO junior 2016). I admit that this one stumped me. Can you figure it out? Solution presented: post by Thomas Hill on Quora https://www.quora.com/In-a-triangle-ABC-AB-AC-angle-BAC-100-circ-Let-D-be-a-point-such-that-B-is-an-interior-point-of-AD-and-AD-BC-How-can-you-find-angle-BDC Other solutions http://jwilson.coe.uga.edu/EMT668/EMT668.Folders.F97/Rapley/EMT725/100deg/100deg.html http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Wise/essay1/essay1.htm https://gogeometry.blogspot.com/2011/11/problem-685-isosceles-triangle-100-40.html pic.twitter.com/NNSkNX2I5w — José Luis da Vila (@jldavilaa01)

Thanks to Ryan from India for the suggestion! Two candles of equal height but different thickness are lit. The first burns off in 8 hours and the second in 10 hours. When will the first candle be half the height of the second? Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many

Can you solve this neat geometry puzzle? Thanks to Joe M. for the suggestion! Sources https://brilliant.org/practice/circle-properties-level-2-3-challenges/?problem=day-5-five-golden-circles&subtopic=circles&chapter=circle-properties How I’m Learning to Step into Math Problems Circle puzzle Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos.

Thanks to Amit from India for the suggestion! A circle is tangent on the exterior of a side of a triangle and tangent to the lines through the other two sides. The tangent side length 7, and the other side lengths are 8 and 9. What is the radius of the circle? 0:00 Problem 1:22

A compilation of Numberphile sound checks – Brady typically asks “what did you have for breakfast” so he can monitor audio levels. More links & stuff in full description below ↓↓↓ Previous sound checks with scientists here: http://youtu.be/4anqDfgQneA Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub

Can you solve this fun little geometry puzzle? Thanks to Roman for the suggestion! Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you buy from the links below I may receive a commission for sales. (As an Amazon Associate

People around the world have asked me this and similar problems. Learn how to solve using only geometry (and a little bit of algebra). There are many other ways to solve the problem too https://www.mathalino.com/reviewer/plane-geometry/02-area-common-arcs-quarter-circles Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many

Matt Parker explores the work of William Shanks – and boots up the ShanksBot. More links & stuff in full description below ↓↓↓ Matt Parker’s 2022 Pi Day Video: https://youtu.be/dtiLxLrzjOQ Discussing William Shanks on Objectivity: https://youtu.be/7yTXMeiVBCc Prime Number playlist: https://bit.ly/PrimePlaylist Pi playlist: http://bit.ly/PiPlaylist Matt Parker website: https://standupmaths.com Numberphile is supported by the Mathematical Sciences Research

Thanks to Victor for the suggestion! A version of this problem appeared on a Kangaroo math competition for 12-13 year olds. Can you figure it out? Special thanks this month to: Michael Anvari, Daniel Lewis, Robert Zarnke, Kyle, Mike Robertson. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Original Math Kangaroo question on YouTube Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1

Our Pi Playlist (more videos): http://bit.ly/PiPlaylist How accurately can we calculate Pi using hundreds of REAL pies? More links & stuff in full description below ↓↓↓ Extended version of this video (director’s slice) at http://www.youtube.com/watch?v=x4kyFKyCMv0 This video features Matt Parker: https://twitter.com/standupmaths Matt believes this is the world’s most accurate pie-based Pi calculation. More Pi videos:

At first glance I thought these integrals would be nearly impossible to solve. But there is a technique where you can solve them nearly instantly! Vedantu JEE YouTube channel BlackPenRedPen video Math StackExchange https://math.stackexchange.com/questions/166553/how-is-the-integral-of-int-abfxdx-int-abfab-xdx Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Why are some

17 is the minimum number of clues required to give a unique sudoku solution – but how did mathematicians prove this? Featuring James Grime. More links & stuff in full description below ↓↓↓ Dr James Grime discusses a recent paper which cracked the problem. The paper being discussed by McGuire and others is at http://arxiv.org/abs/1201.0749

Cliff Stoll is passionate about Klein Bottles. More links & stuff in full description below ↓↓↓ Don’t miss the video about how he uses a robot to store 1,000 bottles UNDER his house… https://youtu.be/-k3mVnRlQLU More videos on Klein Bottles: http://bit.ly/KleinBottles ACME Klein Bottles: http://bit.ly/ACME_Klein Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: