This problem comes from an exam in 1888 for secondary school students. It was actually optional so it was considered to be a challenging problem. I bet some students today will struggle with it too, but it’s the kind of problem solving I think we should all learn. Can you figure it out? Original exam

John H Conway on his love/hate relationship with his most “famous” invention. More on how he invented it at: http://youtu.be/R9Plq-D1gEk More links & stuff in full description below ↓↓↓ 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 Mathematical Sciences Research Institute

How many triangles are too many? Featuring Henry Segerman from Oklahoma State University. More links & stuff in full description below ↓↓↓ Check Henry’s book about 3D printing math: http://amzn.to/2cWhY3R More Henry videos: http://bit.ly/Segerman_Videos Henry’s hinged doilies were joint work with Geoffrey Irving (https://naml.us) Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook:

At first I thought this problem was a mistake because it seemed impossible to solve! I have discovered a truly remarkable proof of this problem which this margin is too small to contain…but no worries I don’t keep secrets: you can watch the video for a solution. Thanks to all patrons! Special thanks this month

Steve Mould (tau) and Matt Parker (pi) go head-to-head. More links & stuff in full description below ↓↓↓ See our tau video: http://www.youtube.com/watch?v=83ofi_L6eAo And check our Pi videos: http://www.youtube.com/playlist?list=PL4870492ACBDC2E7C Matt Parker: http://www.standupmaths.com/ Steve Mould: http://www.stevemould.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

This is a delightful problem. Find the area of the triangle defined by the four squares. It seems impossible but it can be solved with the right perspective. Can you figure it out? Sources Puzzle by Catriona Shearer The area of the bottom left square is 5. What’s the area of the blue triangle? pic.twitter.com/nBR32b760x

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

French numbers can pose problems for non-native speaker – especially when you move beyond 70. Also discussing problems with phone numbers and commas! More links & stuff in full description below ↓↓↓ Featuring Dr Paul Smith from the University of Nottingham. The French and marks out of 20: http://www.youtube.com/watch?v=QzrRkhU248A A little extra unlisted bit from

A little extra trick based on some of the Mobius cutting videos we recently published. Featuring Tadashi Tokieda. More links & stuff in full description below ↓↓↓ MORE: http://bit.ly/tadashi_vids 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 Mathematical Sciences Research Institute

Here’s the video everyone requested after the average distance in a square video. What’s the average distance of two points on a circle? Can you figure it out? Cleve Moler post – average distance two points in a square https://blogs.mathworks.com/cleve/2017/09/25/how-far-apart-are-two-random-points-in-a-square/ My video – average distance two points in a square Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch

Hotelling’s game explains why gas stations are close to each other and why politicians appeal to the central voter during elections. Blog post (Hotelling’s game): http://wp.me/p6aMk-37 Blog post (applied to why Donald Trump gets so much media coverage): http://wp.me/p6aMk-4yA If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions Connect on social media.

The Monster Group explained. More links & stuff in full description below ↓↓↓ Featuring John Conway (Princeton University) and Tim Burness (University of Bristol). Brown papers and Numberphile artwork: http://bit.ly/brownpapers More Conway on this topic: http://youtu.be/xOCe5HUObD4 And Conway on Game of Life, etc: http://bit.ly/JohnConway A little extra bit from Tim: http://youtu.be/MXKiih4JJvQ Support us on Patreon:

Lacking proper equipment, two friends devise a way to measure how long the train is based on their walking steps. Can you solve for the length of the train? Thanks to Pedro for suggesting this problem! 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 channel to feature math topics

The tin asks: “What’s the biggest number you can make?” Sounds like a challenge! More links & stuff in full description below ↓↓↓ Ebay link: AUCTION OVER Fate of the spaghetti (not pleasant): http://youtu.be/tsbHenS5CUs Brady reads the whole number: http://youtu.be/uN2U9PQUGB0 The people at Heinz had nothing to do with his video – I just saw

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:

L-Functions are likely to play a key role in proving the Riemann Hypothesis, says Professor Jon Keating from the University of Bristol. More links & stuff in full description below ↓↓↓ L-Function & Modular Form database: http://www.lmfdb.org Prime Number and Riemann Hypothesis playlist: http://bit.ly/primevids Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook:

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

Why number 1 is the “leading digit” more often than you may expect? More links & stuff in full description below ↓↓↓ See us test the law using Brady’s YouTube viewing figures at: http://youtu.be/VbtNy54ya9A Blog about all this at: http://bit.ly/benfordslaw Brown Paper from this video on ebay: http://bit.ly/brownpapers This video features Steve Mould: http://www.stevemould.com/ and

Brady’s view on people who write: “FIRST” – http://youtu.be/CmRh9tFYC68 More links & stuff in full description below ↓↓↓ Dr James Grime on the Pisano Period – a seemingly strange property of the Fibonacci Sequence. Available Brown papers: http://periodicvideos.blogspot.co.uk/2013/09/brown.html With thanks to http://www.youtube.com/AlanKey86 James Grime on Twitter: https://twitter.com/jamesgrime The Alan interview: http://www.youtube.com/watch?v=acTrvMlpuxA Lagrange Points: https://www.youtube.com/watch?v=mxpVbU5FH0s NUMBERPHILE

A convex quadrilateral is divided into four parts by its diagonals. Three of the areas are 2, 1, and 3 as shown in the diagram. What is the area of the fourth region? Thanks to Gerrit for sending me this geometry problem and a solution! You guys have really been sending me a lot of

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

What value is each letter? This is an incredible math problem with just a single solution! Can you figure it out? My blog post for this video https://wp.me/p6aMk-85e Websites consulted http://mathforum.org/library/drmath/view/60417.html https://en.wikipedia.org/wiki/Verbal_arithmetic#Solving_cryptarithms Playlist to watch all videos on MindYourDecisions This is the only channel to feature math topics suggested by people around the world. Support

Check our sponsor The Great Courses Plus (free trial): http://ow.ly/j5cB30hIvm2 This video features Cliff Stoll. More links & stuff in full description below ↓↓↓ More Cliff Stoll videos: http://bit.ly/Cliff_Videos Buy a Klein Bottle from Cliff – it’s an experience: http://www.kleinbottle.com Discuss this video on Brady’s subreddit: https://redd.it/96x6c4 Numberphile is supported by the Mathematical Sciences Research

Thanks to Eric from Miami for suggesting this problem and sending a solution! The diagram shows a quadrilateral ABCD with the values for some angles and the length of AB. Can you figure out the area of ABCD? 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 My blog post for this video https://wp.me/p6aMk-85A