Math

The Josephus Problem, featuring Daniel Erman from University of Wisconsin-Madison. Winning at Dots and Boxes: https://youtu.be/KboGyIilP6k More links & stuff in full description below ↓↓↓ Correction: Around 9:40 that should be L less than 2^a NOT 2a — Sorry, typo in editing! But you got the point hopefully. Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website:

Some students in Finland missed out on 1000 euros because they missed this problem! Sources for problem https://old.reddit.com/r/math/comments/cy7u04/a_very_simple_but_tricky_question_from_finnish/ @rizka commented with a link to the 2014 exam (in Finnish). It is question 4: https://yle.fi/progressive/fynd/oppiminen/oppiminen.yle.fi/yo-kokeet/matematiikka_pitka.pdf Quadratic equation history (Brahmagupta) https://www-history.mcs.st-and.ac.uk/HistTopics/Quadratic_etc_equations.html https://en.wikipedia.org/wiki/Quadratic_equation#History Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?Subscribe https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Click to watch all

I bet this one will give many adults a good challenge too. Thanks to Pett for the suggestion! Special thanks this month to: Kyle, Mike Robertson, Michael Anvari, Daniel Lewis, Robert Zarnke. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Singapore International Math Olympiad Challenge (SIMOC) 2015 – Primary 5 Paper, problem 24. Sample Papers Subscribe:

More links & stuff in full description below ↓↓↓ Brady’s Movember Page: http://bit.ly/BradyMo See full description for list of Connect 4 links. John Tromp’s page: http://bit.ly/TrompNumberphile James Allen’s Connect Four book: http://bit.ly/AllenBook James Allen: http://james.fabpedigree.com/ OEIS: https://oeis.org/A212693 Victor Allis paper: http://bit.ly/AllisPaper 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

What is 7×8? This video teaches how you can use your hands to multiply two numbers between 6 and 10 using your fingers. Here’s the reason the method works: https://www.youtube.com/watch?v=eEao6-F7fz8 If you like my videos, you can support me at Patreon: https://www.patreon.com/mindyourdecisions Connect on social media. I update each site when I have a new

Johnny Ball on the “often missed” Hippocrates of Chios. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ More on Johnny Ball, including his books and live shows: https://www.johnnyball.co.uk See Johnny discuss Russian multiplication: https://youtu.be/HJ_PP5rqLg0 Numberphile is supported by the Mathematical Sciences Research Institute

This problem is adapted from the first round of the 2017 Dutch Maths Olympiad. Special thanks this month to: Robert Zarnke, Marq Short, Kyle, Mike Robertson, Michael Anvari. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Reddit Math Riddles Simple square puzzle byu/Irratix inmathriddles Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many

Matt Parker talks about numbers – as he often does. His book “Humble Pi” is at: http://bit.ly/Humble_Pi More links & stuff in full description below ↓↓↓ The book on Amazon: https://amzn.to/2NKposg Numberphile podcast is on your podcast player. Or the website is: https://www.numberphile.com/podcast And it’s on YouTube too: http://bit.ly/Numberphile_Pod_Playlist The Knight’s Tour T-Shirt is in

Dr James Grime is back and talking about tortoises. More links & stuff in full description below ↓↓↓ In many ways this video follows on from http://www.youtube.com/watch?v=bFNjA9LOPsg and then http://www.youtube.com/watch?v=CMP9a2J4Bqw James Grime’s website is: http://singingbanana.com 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

Thanks to Jumar for the suggestion! Can you solve this interesting geometry problem? 0:00 Problem 1:10 Similar triangles 2:29 Solution 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

If a semicircle and its flipped copy are placed side by side, how much distance do they span from end to end? This is a neat problem adapted from a Mathematical Olympiad Qualifying Test in the Philippines. Can you figure it out? Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos).

Professor Tony Padilla is back with another epic number. Our Big Number playlist of previous videos: http://bit.ly/Big_Numbers More links & stuff in full description below ↓↓↓ Busy Beavers on Computerphile: https://youtu.be/CE8UhcyJS0I With thanks to Agustín Rayo himself. Read more from Prof Rayo at: http://web.mit.edu/arayo/www/bignums.html And see his website at: https://arayo.scripts.mit.edu/home/ Tony Padilla: https://twitter.com/DrTonyPadilla Numberphile is

Featuring Neil Sloane… Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Trapped Knight T-Shirt: https://teespring.com/en-GB/numberphile-trapped-knight Neil Sloane is creator of the On-Line Encyclopedia of Integer Sequences: https://oeis.org For more on the sequences and diagrams in this video, you can start at: https://oeis.org/A316667

Can you solve this geometry problem? Thanks to Lucas from Brazil for the suggestion! Kangaroo Maths 2020 https://www.matematica.pt/en/docs/kangaroo/enunciados/2020/2020_Grade9-10.pdf Proof of inscribed angle theorem https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-inscribed-angles/a/inscribed-and-central-angles-proof 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

Featuring Grant Sanderson, creator of 3blue1brown. Extra footage from this interview: https://youtu.be/pJyKM-7IgAU 3blue1brown video on the shadow a cube: https://youtu.be/ltLUadnCyi0 More links & stuff in full description below ↓↓↓ 3blue1brown: https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw Grant on The Numberphile Podcast: https://youtu.be/A0RH93XvSyU Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox,

Thanks to Devesh from India for the suggestion! A version of this problem was given in an Olympiad qualifying test. Socratic https://socratic.org/questions/a-root-a-b-root-b-183-a-root-b-b-root-a-182-find-9-5-a-b Math StackExchange https://math.stackexchange.com/questions/2405256/find-the-value-of-frac95ab-given-that-a-sqrtab-sqrtb-183-and-a Brainly https://brainly.in/question/3901575 Quora https://www.quora.com/Suppose-a-b-are-positive-real-numbers-such-that-a%E2%88%9Aa-+-b%E2%88%9Ab-183-a%E2%88%9Ab-+-b%E2%88%9Aa-182-How-do-we-find-9-5-a-+-b 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

The Prime Number Theorem shows that primes are like weeds, popping up everywhere! Dr James Grime explains — Little bit extra cut from this video: http://youtu.be/TMRZYSQGAcw More links & stuff in full description below ↓↓↓ Our prime number video collection: http://bit.ly/primevids Follow James on Twitter at: https://twitter.com/jamesgrime NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile

Recently Russia’s Prime Minister Mikhail Mishustin visited 11th grade students (about 17-18 years old) and asked them a challenging geometry problem. Can you figure it out? I came across this puzzle in Alex Bellos’s column on The Guardian. He has a new book that I wanted to share titled “The Language Lover’s Puzzle Book.” I

An evil warden holds you prisoner, but offers you a chance to escape. There are 3 doors A, B, and C. Two of the doors lead to freedom and the third door leads to lifetime imprisonment, but you do not which door is what type. You are allowed to point to a door and ask

Is 1 a prime number? Apparently not. Dr James Grime explains. More links & stuff in full description below ↓↓↓ James Grime’s website is: http://singingbanana.com/ 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/ Sign

This problem is baffling many people on Facebook and Twitter. Can you figure it out? I thank everyone who emailed it to me, with a special thanks to the first two people: Riadh Temala from Tunisia; and Shivam Varma from India. 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

Tadashi explores a special set of dice… And has a powerful lesson. More links & stuff in full description below ↓↓↓ Subscribe to Numberphile: http://bit.ly/Numberphile_Sub More dice videos: http://bit.ly/Dice_Videos Playlist of Tadashi Tokieda videos: http://bit.ly/tadashi_vids Want to buy some dice like this – our friends at Maths Gear have some: http://bit.ly/MathsGearDice Discuss this video on

Extended math version: http://youtu.be/ugbWqWCcxrg?t=2m32s A version for Dummies: https://youtu.be/7u6kFlWZOWg More links & stuff in full description below ↓↓↓ This video features Lisa Goldberg, an adjunct professor in the Department of Statistics at University of California, Berkeley. 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 Numberphile is

In a square, a line is drawn from the bottom left corner with length 12 to the interior of the square. From the end of that line, a perpendicular is drawn going up and left with length 3. From the end of that line, another perpendicular is drawn going up and right with length 9.

Featuring Professor Edward Frenkel. Here is the biggest (?) unsolved problem in maths… The Riemann Hypothesis. More links & stuff in full description below ↓↓↓ Prime Number Theorem: http://youtu.be/l8ezziaEeNE Fermat’s Last Theorem: http://youtu.be/qiNcEguuFSA Prof Edward Frenkel’s book Love and Math: http://amzn.to/1g6XP6j Professor Frenkel is a mathematics professor at the University of California, Berkeley – http://edwardfrenkel.com

This is a nice little logic puzzle from Terry Stickels! Books by Terry Stickels (including “Contemporary Brainteasers”) http://www.terrystickels.com/books.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

A bit about zero – including a discussion of its even-ness!? More links & stuff in full description below ↓↓↓ Featuring Dr James Grime (https://twitter.com/jamesgrime) and Professor Roger Bowley (University of Nottingham). 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

Thanks to John H. for the suggestion! A square is inscribed in a quarter circle with two of its vertices on the arc. If the radius equals 1, what is the area of the square? Special thanks this month to: Robert Zarnke, Kyle, Mike Robertson, Michael Anvari, Daniel Lewis. Thanks to all supporters on Patreon!

What is the area of the square? Thanks to Papa in India for the suggestion! This puzzle is half of of problem 21 in the 2017 AMC 10A. https://artofproblemsolving.com/wiki/index.php/2017_AMC_10A_Problems/Problem_21 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

Famously beautiful, the Mandelbrot Set is all about complex numbers. Featuring Dr Holly Krieger from MIT. More links & stuff in full description below ↓↓↓ The next part is on Numberphile2 at: http://youtu.be/oCkQ7WK7vuY Animation courtesy of team fresh. Check out more at: http://hd-fractals.com — Music: Alan Stewart. Support him at http://bit.ly/1sdwTHF More videos with Holly

Fermat’s “Little” Theorem is great – but beware of Fermat Liars and tricky Carmichael Numbers. More links & stuff in full description below ↓↓↓ Continues at: http://youtu.be/HvMSRWTE2mI Featuring Dr James Grime – https://twitter.com/jamesgrime 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 Numberphile is supported by the

To complete a job, it takes: Alice and Bob 2 hours, Alice and Charlie 3 hours, and Bob and Charlie 4 hours. How long will the job take if all 3 work together? Many, many US college students set up the equations incorrectly and get the wrong answer. Can you solve it? Watch the video

Learn one weird trick to solve this problem! Thanks to Nestor Abad for alerting me of a typo in an earlier version of the video. Reference https://socratic.org/questions/if-x-sqrt-x-2-1-y-sqrt-y-2-1-1-what-is-x-y 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

Dividing by zero, zero divided by zero and zero to the power of zero – all pose problems! More links & stuff in full description below ↓↓↓ This video features Matt Parker and James Grime – https://twitter.com/standupmaths and https://twitter.com/jamesgrime 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

Dr James Grime discusses a couple of clever formulas which are pandigital – using all the numbers from 1-9. More links & stuff in full description below ↓↓↓ More on pandigital numbers: https://youtu.be/gaVMrqzb91w More on e: https://youtu.be/AuA2EAgAegE More James Grime videos: http://bit.ly/grimevideos Book James for a talk: http://jamesgrime.com The contest which gave us these formulas:

Can you solve this equation? Thanks to Hrigved for the suggestion! Reference https://math.stackexchange.com/questions/438452/find-all-real-numbers-such-that-sqrtx-frac1x-sqrt1-frac1x 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

Can you estimate the log of 3 to the base of 2 without using a calculator? This kind of skill is actually pretty important in university mathematics. Watch the video to learn how to solve it! Source https://www.quora.com/How-do-you-solve-this-question-from-Oxfords-Math-Admissions-Test-No-calculators 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

Matt Parker reveals his pride and joy – the mysterious Parker Square! More links & stuff in full description below ↓↓↓ Merch: https://numberphile.creator-spring.com/listing/the-parker-square More magic square videos: http://bit.ly/MagicSquareVideos Matt Parker: https://www.youtube.com/standupmaths Audrey (Brady’s chihuahua): https://youtu.be/s84dBopsIe4 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 Numberphile is supported

Many tests around the world include a problem like this. How can you calculate this quickly, without making any mistakes? Thanks to all patrons! Special thanks to: Ertugrul Oruç, Michael Anvari, Richard Ohnemus, Shrihari Puranik, Kyle. Source https://twitter.com/thebapex/status/1149020375189270528 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

A game to play on the elliptical table: http://youtu.be/3WHBlPvK3Ek More links & stuff in full description below ↓↓↓ And more extra footage: http://youtu.be/pulp55gTKGE Alex Bellos’ Loop Table website: http://www.loop-the-game.com Alex discusses the topic in his book Alex Through the Looking-Glass (UK) and The Grapes of Math (US)… http://bit.ly/BellosBooks Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website:

Marcus du Sautoy discusses Gödel’s Incompleteness Theorem More links & stuff in full description below ↓↓↓ Extra Footage Part One: https://youtu.be/mccoBBf0VDM Extra Footage Part Two: https://youtu.be/7DtzChPqUAw Professor du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford. Professor du Sautoy’s book as mentioned… In

Can you solve this tricky math problem? Thanks to Asad for the suggestion! Art of Problem Solving 2019 AIME Problem 3 (there are many solution methods) https://artofproblemsolving.com/wiki/index.php/2019_AIME_I_Problems/Problem_3 Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I cannot reply to everyone but I consider all ideas! Like many YouTubers I use popular software to

Thanks to Surjadi from Indonesia for the suggestion! Twitter Cshearer41 A square is split into five rectangles with equal areas. What’s the area of the square? pic.twitter.com/wtuEjxMASI — Catriona Agg (@Cshearer41) July 11, 2020 solution by @birkhofyan pic.twitter.com/3EIij7DjaU — Birkan Yıldız (@birkhoff_math) July 11, 2020 Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video).

Catch David on the Numberphile podcast: https://youtu.be/9y1BGvnTyQA Professor David Eisenbud on the infamous Collatz Conjecture, a simple problem that mathematicians may not be “ready” to crack. More links & stuff in full description below ↓↓↓ Extra footage from this interview: https://youtu.be/O2_h3z1YgEU Prof Eisenbud’s 17-gon: https://youtu.be/87uo2TPrsl8 Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on

We now have a Tumblr: Tumblr: http://numberphile.tumblr.com This paper on ebay: http://www.ebay.co.uk/itm/221197137799? More links & stuff in full description below ↓↓↓ Just how hard was the second problem cracked by Will in Good Will Hunting? Matt Damon! And who doesn’t love Homeomorphically Irreducible Trees? This video features Dr James Grime – http://singingbanana.com/ Music by Alan