# Math

Thanks to Alessio from Italy for creating this problem and sending it to me! A cyclist and a series of motorcycles are racing to the top of a long climb, and the cyclist doubles back. Given…

This question has generated a lot of debate online. BuzzFeed’s video has 450000+ views already. But the question has a mathematical interpretation with a correct answer: in topology, how many…

In honor of the holiday, let’s do some math! Interestingly George Washington and Abraham Lincoln both understood the value of mathematics. And amazingly manuscripts of their homework have survived…

It’s not the famous Cheryl’s birthday problem…According to Mothership, this math problem is causing a lot of confusion: “There are 37 students in a class. How many students, at the least,…

With Dr Holly Krieger from Murray Edwards College, University of Cambridge. Have a look at Brilliant (and get 20% off) here: https://brilliant.org/Numberphile More links & stuff in full descriptio…

Here’s a mysterious puzzle you could share with a special person. If ∑8dh = loan, and ∓8rΠ = torii, then what is 128√e980 = ? I usually mention sources. The 128√e980 is a meme whose…

Little known fact: Abraham Lincoln was a very good math student! In this video I share the story of why he studied Euclid’s Elements. I also share a problem he did while in school. He did in…

Media outlets around the world went crazy over a 5th grade math exam question in China. But they all missed the real story! The problem actually dates back to French researchers in 1979. In…

HUGE thanks to Stephen Lerantges for solving the problem! A glass has an inner diameter of 10 cm and inner height of 10 cm. Each of the 4 balls has a diameter of 5 cm. How much water do you…

Media outlets around the world are reporting on these math problems that have “flummoxed” everyone. As these got so much attention, I wanted to share some of the headlines and give a small…

The Great Courses Plus (free trial): http://ow.ly/C3FE30hIvhc This video features Dr James Grime. More links & stuff in full description below ↓↓↓ More James Grime on Numberphile: http://bit…

This problem stumped me! But it has an unbelievably elegant solution. Take any equilateral triangle and pick a random point inside the triangle. Draw from each vertex a line to the random…

Get 10% off at Squarespace: https://www.squarespace.com/numberphile This feature features Ben Sparks… More links & stuff in full description below ↓↓↓ Ben Sparks Twitter: https://twitter.c…

On January 22, 2018, Facebook Open Source tweeted to announce the “flick,” a unit of time to help sync various video frame rates and audio sampling frequencies. The media loved the story and…

Featuring Professor Günter Ziegler, who was visiting at MSRI. Extra footage at: https://youtu.be/FHkaN9FOzUY More links & stuff in full description below ↓↓↓ This video features Professor…

Thanks to Halvor Kjærås for creating this logic puzzle! Barney says he caught 5 fish, and Alfred says he caught 2. But each person fibs about numbers when spoken aloud. Can you figure out…

Thanks to Kristian from Norway for sending me this problem! A three digit number is re-written with multiplication symbols between the digits, and the product is equal to one-fifth the original…

Check out https://brilliant.org/numberphile (20% off premium subscription) This video features Ben Sparks. More links below ↓↓↓ Ben Sparks website: https://www.bensparks.co.uk More of…

The Online Math Olympiad is a contest for high school students with challenging problem. This 2016 test had an average score of 9 out of 30. This video is an adaption of problem 16 which is…

Matt Parker discusses a problem involving Square Sums. Go deeper with extra footage: https://youtu.be/7_ph5djCCnM More links & stuff in full description below ↓↓↓ More Matt Parker on…

The number N = 69720375229712477164533808935312303556800 is special – it is the smallest number that has all numbers 1 to 100 as factors. The puzzle: what is the prime factorization…

This problem comes from a national exam in Malaysia. A cylindrical container with length 20 cm is placed on the floor against the wall as shown in the diagram. Point Q is on the edge of the…

Discussing vertex covers and Alcuin numbers for graphs – and a famous old puzzle. Filmed at MSRI with Dr Annie Raymond. More links & stuff in full description below ↓↓↓ Annie Raymond:…

Follow the simple instructions in the video and the result will be a fun mathematical effect! The trick got really popular a couple of years ago, but no one explained exactly why it worked….

This is a fun little geometry problem inspired by a suggestion from Yossi Rozhenko. If the red area equals the blue area, what is the value of: (large circle’s radius)/(small circle’s radius)?…

Luuk stumped his math teacher with one of my puzzles. Then his math teacher gave him a problem that Luuk suggested to me. If AAA + BBB + CCC = BAAC, what is the value of each digit? The digits…

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…

This is a video I made a long time ago but forgot to publish! Consider this puzzle as a bite-size holiday bonus. A rectangle is divided into 4 rectangles, and you know the areas of 3 of them…

This is a challenging problem that ultimately works out pretty nicely. A circle with radius 1 is tangent to two points of the parabola y = x^2. What is the area between the circle and the parabola?…

This video features Dr Hannah Fry (more links below) ↓↓↓ Check out Brilliant.org: https://brilliant.org/numberphile (20% off premium subscription) That circle cutting problem on Brilliant:…

This is one of those puzzles that seems completely impossible to solve at first, but it has a delightful solution. Thanks to Oskar for sending me this! The problem appeared on an early round…

One of the most famous stories from the sort of cricket involves numbers, averages, and a duck. More links & stuff in full description below ↓↓↓ Archive footage courtesy of AP Archive:…

A kite is placed in a square, can you figure out one of its angles? I made a video for this “impossibly hard” problem from a New Zealand maths exam. But it turned out my proof had a flaw, which…

I WAS WRONG! This video shows the correct answer, but there was a slight flaw in the proof presented so I made a new video to correct it. You can watch this video first, or just watch the new…

Cliff explains his passion for two Friden EC-132s. Extra discussion and explanation at: LINK More links & stuff in full description below ↓↓↓ More Cliff videos: http://bit.ly/Cliff_Videos…

A system of equations involving a pair of shoes, a cat, and whistles is the latest math problem that people are arguing about, and it has gone viral on social media sites. The problem was given…

This problem was part of a written interview test for Amazon in India. A drawer contains 12 identical black socks and 12 identical white socks. If you pick 2 socks at random, what is the probabilit…

A maths test in New Zealand is causing a lot of controversy because many students felt it was too hard. The story is getting huge coverage in New Zealand and even in some British and American…

Solve for area of the circle that is centered at the origin (0, 0) that is inscribed between the bell curves with equations y = e^(-x^2) and y = -e^(-x^2). Can you figure it out? Watch the…

Using a kamifusen (a Japanese paper balloon). Featuring Tadashi Tokieda. More Tadashi videos: http://bit.ly/tadashi_vids More links & stuff in full description below ↓↓↓ Objectivity…

James Grime is back and talking prime numbers. Check out Brilliant.org by using the link: https://brilliant.org/numberphile (20% off premium subscription) More on prime numbers: http://bit.ly/prim…

I have found three consecutive integers such that their product is equal to their sum. What could my numbers be? Solve for all possibilities. Then watch the video for a solution. I thank Ken…

This is a fun problem that appeared in UKMT, an organization that organizes maths competitions and educational activities. What is the following equal to? Give your answer as an integer. (10!…

Preston McAfee is the chief economist at Microsoft. More links & stuff in full description below ↓↓↓ Benford’s Law: https://youtu.be/XXjlR2OK1kM Preston McAfee: http://www.mcafee.cc…

This clock displays time accurately like any other 12 hour clock. But this clock has no numbers, and the clock has been rotated out of position. Based on the position of the hour and minute…