# Math

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…

Katie Steckles on Pancake Numbers.. Signup for your FREE trial to The Great Courses Plus here: http://ow.ly/EJwH30fiZ1d More links & stuff in full description below ↓↓↓ More Numberphile…

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…

Professor Tony Padilla on the epic number, TREE(3). Continues at: https://youtu.be/IihcNa9YAPk More links & stuff in full description below ↓↓↓ Graham’s Number: http://bit.ly/G_Number…

This challenging problem was given to 8th graders in Russia, but it stumped me! The question was presented as text only–no diagram. Also, the problem was part of an entrance exam for a selective…

Home base is defined by a geometric construction. Take a square whose side is 17″ and then remove two corners. The adjacent sides are 8.5″, and the two remaining sides are 12″ and meet at a…

When Cliff Stoll sets your homework, there’s always an extra lesson. More links & stuff in full description below ↓↓↓ More Cliff videos: http://bit.ly/Cliff_Videos Cliff’s Klein Bottles:…

This puzzle went viral in the discrete mathematics community because so many people got it wrong! You roll a fair dice until you get a 6. What is the expected number of rolls, including the…

“Jess wants 200 ribbons of length 110 centimeters for a party. However, the ribbons were sold at 25 meters per tape. How many tapes will Jess need?” Yahoo News reports many adults find this…

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 Numberphile videos with…

What is 6 + 66 + 666 + … + 666…6? Each new number has one more digit equal to 6, and the last number has 666 digits of 6. Watch the video for a solution. My blog post for this video (includes…

Juggling with Colin Wright. More links & stuff in full description below ↓↓↓ Colin Wright on Twitter: https://twitter.com/colinthemathmo Numberphile is supported by the Mathematical…

Audible (30-day trial, free audio book): https://www.audible.com/numberphile More links & stuff in full description below ↓↓↓ This video features Dr Hannah Fry. More videos with Hannah:…

Can you count the number of rectangles in the grid? How about in the L-shaped grid? These problems appeared on the TV show Superhuman hosted by Kal Penn (Kalpen Modi). The contestant Summer…

Squarespace (including 10% off): https://www.squarespace.com/numberphile Video features Matt Parker. More links & stuff in full description below ↓↓↓ Parker CIRCLE T-Shirts and Mugs…

Dave Carpenter sent me this problem by email and it’s a really fun problem–I actually miscalculated the answer on my first attempt! If eight ants on corners of a cube each randomly move to…

Cliff wants to tell a story on a Möbius strip… And discusses recursive hot chocolate!? More links & stuff in full description below ↓↓↓ More Cliff Stoll videos: http://bit.ly/Cliff_Videos…

Dr James Grime and a handy trick for checking calculations. Ditch the nines… More links & stuff in full description below ↓↓↓ Some extra footage from this interview: https://youtu.be/wQsQ…

When is n² + 45 equal to a perfect square, for n a positive integer? I received this MathCounts problem by email from Bill by email. Can you figure it out? Watch the video for a solution….

A prime number “gift” from a mathematicians leaving his college. More links & stuff in full description below ↓↓↓ Featuring Tadashi Tokieda. More Tadashi: http://bit.ly/tadashi_vids…

What is the sum of the series 1/(1×2) + 1/(2×3) + 1/(3×4) + … ? This problem was part of the Cambridge Exam in 1802. Can you figure it out? Watch the video for a solution. Thanks to all…

How predictable are you? Pick a 3 digit number with 3 different digits. Now reverse the digits to get a new number. You now have two numbers. Subtract the smaller number from the larger number….

Four circles of equal size are inscribed in a square as shown in the video diagram. Inside of the four circles is a smaller square tangent to each of the four circles. If the large square has…