# Math

Which figures can you form from the two shapes A and B? This is a sample question from the 2017 NAEP for 8th grade US students. Be sure to select all of the …

Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor)… More links & stuff in full description below ↓↓↓ Check …

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 …

Thanks to Oladele from Nigeria for suggesting this problem! Team A has 4 girls and 7 boys. Team A takes 5 days to paint 4 rooms. Team B has 7 girls and 10 …

Many people emailed me this apparent paradox showing 4 = 2. Can you figure out where the mistake is? My blog post for this video https://wp.me/p6aMk-80Q …

Thanks to Mike Painter for emailing me! This problem comes from a 1957 math class. A man is standing due East of a tower and notes it subtends an angle of 45 …

The Cooperative Bank of Kenya, one of Kenya’s largest banks, tweeted out this problem. If 4 + 2 = 26, 8 + 1 = 79, 6 + 5 = 111, then what is 7 + 3 = ?

Check out Brilliant (and get 20% off) by clicking https://brilliant.org/numberphile (sponsor) Hannah Fry has a new book coming: https://amzn.to/2J6oCph (US) or …

Hippocrates of Chios solved this, nearly 100 years before Euclid even wrote The Elements, and before we knew the exact formula for the area of a circle. This is …

Thanks to George who sent me this problem (created by 7th grade math teacher Ms. V)! There is a table in the video. The numbers in the first column are …

Discussing h-vectors and the g-conjecture. Featuring June Huh from the Institute for Advanced Study at Princeton University. More links & stuff in full description …

Thanks to Brian Galebach who created and sent me this problem! You arrive at a park where geysers A, B, and C erupt at intervals of precisely 2, 4, and 6 hours, …

Signup for your free trial to The Great Courses Plus here: http://ow.ly/b5wA30hIviV (sponsor) More links & stuff in full description below ↓↓↓ James Grime on a …

Another day, another viral math problem! Lighthouses A, B, and C turn on and off in regular intervals. A shines light for 3 seconds, then is off for 3 seconds, and …

Limited edition “Golden Ratio” T-Shirts at Fibonacci prices: https://teespring.com/NP-Seeds and https://teespring.com/NP-Golden-Rectangle More links & stuff in …

Thanks to Tim for sending this problem! The total amount of sand contained in Boxes A, B and C is 360 grams. First a mathematician pours 1/6 of the sand from …

Check out Brilliant (and get 20% off) by clicking https://brilliant.org/numberphile Featuring Ben Sparks — More links & stuff in full description below …

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…

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