# Math

Some Scottish students felt the National 5 Maths Exam was too difficult, particularly this tricky umbrella question. The test is not yet released, so I have …

Alice and Bob are playing a game. Alice starts by placing a knight on the chessboard. Then they take turns moving the knight to a new square (standard chess …

Featuring Alex Bellos. See the accompanying Dudeney Pentominoes video: https://youtu.be/wZ1E_CM7MqA More links & stuff in full description below …

Featuring Alex Bellos on Polyominoes. See the accompanying coin hexagon video: https://youtu.be/_pP_C7HEy3g More links & stuff in full description below …

Thank you for 100 million views! To celebrate, here’s a puzzle related to 100 million, sent by Karin. Find a sequence of 100 million consecutive non-prime numbers. That is, every number is…

Mathematician Ed Southall, from the University of Huddersfield, created a stir when he tweeted this problem (@solvemymaths). The problem was covered in “The Daily Mail” and “The Sun.” In this…

This was voted on Quora as one of the most difficult SAT math problems. On the SAT you have to solve each math problem in about 1 to 2 minutes. Can you solve this problem quickly? My blog…

Check out Brilliant (and get 20% off) by clicking https://brilliant.org/numberphile Featuring Federico Ardila — More links & stuff in full description below ↓↓↓ Extra footage (the…

Thanks to Ben Craft for sending me this problem and its solution! Find a value of x such that (3 + 4)(3^2 + 4^2)(3^4 + 4^4)(3^8 + 4^8)(3^16 + 4^16)(3^32 + 4^32) = 4^x – 3^x. There’s a really…

New research sheds light on the so-called Hot Hand Fallacy. Featuring Professor Lisa Goldberg. More links & stuff in full description below ↓↓↓ A bit extra from this interview: https://youtu…

Thanks to Kshitij from India for sending me this problem! “A leaf is torn from a paperback novel. The sum of the numbers on the remaining pages is 15000. What are the page numbers on the torn…

Problematic Men is a Korean TV show that featured puzzles solved by contestants, many of whom had genius IQ levels over 150. One of the puzzles was: if 9981 + 1601 = 2957, then 1080 + 9168…

This problem caught the attention of Bollywood celebs, including Sonam Kapoor, Aditi Rao Hydari, and Diana Penty, after fashion magazine editor Jitesh Pillai tweeted it. How many triangles…

This problem is tricky even for people who are good with numbers. Can you make 24 from the numbers 3, 3, 8, 8? You can use the operations + – × ÷ ( ). You have to use all four numbers (the…

More Cliff Stoll videos: http://bit.ly/Cliff_Videos More links & stuff in full description below ↓↓↓ Our first Borromean Ring Video: https://youtu.be/x6Ml4AEt0kk Tadashi does Borromean…

“One day it started snowing in the morning at a heavy and steady rate. A snowplow started out at noon, going 2 miles in the first hour and 1 mile in the second hour. What time did it start…

Featuring Federico Ardila from San Francisco State University – filmed at MSRI. More links & stuff in full description below ↓↓↓ Federico previously on Numberphile: https://www.youtu.be/OfEv…

You’re going to tell me 1 dollar equals 100 cents. But mathematically, 1 dollar is really equal to 1 cent. Don’t believe me? Watch the video for a proof that will blow your mind. In 2006,…

Thanks to Hyeong-jun (H. J.) for emailing me this problem! This is a challenging problem from the math section of the 1997 CSAT, a standardized test in Korea. Can you figure it out? It took…

Lady Karren Brady tweeted this puzzle with a challenge to solve in 3 minutes, and it stumped Piers Morgan, who obviously need to watch MindYourDecisions to learn the order of operations ;)…

Thanks to Daniel from Hungary for sending me this question from a math exam! When empty, a container fills completely from a faucet in A hours. When full, the same container drains completely…

More Ron Rivest videos: http://bit.ly/RonRivest Cryptography playlist: http://bit.ly/crypto_videos More links & stuff in full description below ↓↓↓ Ron Rivest: http://people.csail.mit.edu/ri…

What is the sum of a geometric series for a finite number of terms? What about an infinite number of terms? The video presents an animated proof of the famous formulas. Once you understand…

In a world where simple math problems spark huge debates online…YOU are the last hope to save mathematics. If you like my videos, you can support me at Patreon: https://www.patreon.com/mindyourd…

Thanks to Professor Henk Tijms for this puzzle suggestion! A few years ago I read a probability book by Henk Tijms and really enjoyed it. So I was both surprised and thrilled to get an email…

Katie Steckles dazzles us with Mental Logs. Have a look at Brilliant (and get 20% off) here: https://brilliant.org/Numberphile More links & stuff in full description below ↓↓↓ More…

Thanks to Lucas from Brazil who sent this problem! This is a proof that 3 = 0 using sneaky algebra that I had never seen before (this is a sneaky mistake, not a simple divide by 0 fallacy)….

Thanks to Bill from New York for this suggestion! Bill emailed me a problem asked to 5th graders in China to identify talented students. A few very talented students did solve it in less than…

Featuring Tadashi Tokieda – more Tadashi videos at: http://bit.ly/tadashi_vids More links & stuff in full description below ↓↓↓ Tadashi Tokieda is a Professor of Mathematics at Stanford…

Thanks to James M. for this suggestion! You roll a dice up to 3 times, stopping after any roll you wish. You get paid the value of the roll you stop. If you play optimally, what is your expected…

I saw this on the Saint Louis Science Center Twitter account and I admit, I was not able to figure it out! Can you? My blog post for this video https://wp.me/p6aMk-7Uw Source https://twitter.com/…

Continues with the proof at: https://youtu.be/Or0uWM9bT5w Featuring Zvezdelina Stankova – more videos with her at: http://bit.ly/zvezda_videos More links & stuff in full description below ↓↓↓…

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…