What is the radius of each sphere? Reference http://puzzling.stackexchange.com/questions/41952/nine-identical-spheres-fit-exactly-into-a-cube Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to learn how to make videos. Be prepared–animation […]

# Category Archives: Math

## Solve if you are a “genius” – incredible hexagon puzzle!

Thanks to Elliott Line for the suggestion! Elliott is the editor of a bimonthly puzzle magazine, Enigma, available exclusively to members of Mensa (a high IQ society). Check out his website for many more great puzzles: http://www.elliottline.com/puzzles General solution method on Math StackExchange https://math.stackexchange.com/questions/2336865/area-of-a-hexagon-from-the-distances-of-the-opposite-sides Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I […]

## Belgian Mystery Number

Can you solve this problem asked to 14 and 15 year olds in the Belgian Mathematical Olympiad? Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube […]

## Colouring Knots – Numberphile

Featuring Professor Sylvain Cappell from NYU. Extra footage at: https://youtu.be/NV3EeagyU0Y More links & stuff in full description below ↓↓↓ Merch based on this video: https://teespring.com/numberphile-knots And here: https://teespring.com/numberphile-figure-eight Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with […]

## Square In A 3-4-5 Triangle Puzzle

What is the area of the square? Thanks to Papa in India for the suggestion! This puzzle is half of of problem 21 in the 2017 AMC 10A. https://artofproblemsolving.com/wiki/index.php/2017_AMC_10A_Problems/Problem_21 Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to […]

## Interesting Angle Problem From Peru

Thanks to Juanci for the suggestion! Also thanks to everyone who shared a solution on Twitter. A special thanks to LuisAndrRomero2 who provided the first detailed solution. Special thanks this month to: Michael Anvari, Kyle. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Who can solve this one? I'm working on a video for it and […]

## Challenging Problem Given To 10 Year Old Students

This problem seems like it is impossible to solve because it does not have enough information. If the rectangle has an area of 10, what is the area of the triangle? Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular […]

## Hard Problem For 9 Year Olds In Taiwan

This problem went viral because even teachers had trouble solving it. It even got covered in television news! Can you figure it out? References BlackPenRedPen Twitter Find A, B, C, D, E. This was a 4th-grade math problem in Taiwan that made the news! I remember my friend gave this problem to me from her […]

## Impossible Viral Problem

What is the area of the triangle? References https://old.reddit.com/r/math/comments/51rr52/calculate_the_area_of_the_triangle_abc/ I agree with area=17.186554595799…My solution is at https://t.co/XjhoNYaKIZThanks for a great problem. Does anyone have an elegant solution? — Chris Harrow (@chris_harrow) September 22, 2018 Inscribed Triangle Challenge https://math.stackexchange.com/questions/1936580/how-to-relate-the-perpendicular-line-that-touches-a-circle-and-an-inscribed-tria https://foro.rinconmatematico.com/index.php?PHPSESSID=0dc1be1086008ebf0fec031f3a0ced1b&topic=96792.msg388692#msg388692 https://math.stackexchange.com/questions/1908861/using-trig-identity-to-solve-a-cubic-equation https://en.wikibooks.org/wiki/Trigonometry/The_solution_of_cubic_equations https://en.wikipedia.org/wiki/Law_of_sines Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all […]

## Poncelet’s Porism – Numberphile

Featuring Daniel Litt. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Daniel Litt: https://www.daniellitt.com/ See Daniel previously on Numberphile: https://youtu.be/eYfpSAxGakI Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated […]

## Can You Solve This Logic Puzzle?

This is from a sample paper for the Online Mathematics Challenge 2020. Source THÁCH THỨC TOÁN HỌC TRỰC TUYẾN 2020 – Đề thi mẫu nhóm 9-10 Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You […]

## Ancient Trick To Solve This Puzzle!

Thanks to Taka for the suggestion! This is a fun and challenging geometry problem. Special thanks this month to: Michael Anvari, Kyle. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Source What's the width of the rectangle?#geometry #maths #puzzle pic.twitter.com/FPOod0dKrB — Pangolin (@panbtc) February 25, 2020 Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). […]

## Predators and Prey – Numberphile

Tom Crawford talks foxes and rabbits. More links & stuff in full description below ↓↓↓ More of Tom on Numberphile: http://bit.ly/TomPlaylist Tom’s website: https://tomrocksmaths.com Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. […]

## Beautiful Solution – Think Inside The Box!

Thanks to Hriden for the suggestion! A version of this problem was given to class 8 students in India (~13 years old). Can you solve for the area of ABCD? Special thanks this month to: Michael Anvari, Kyle. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). […]

## Overlapping Rectangles Puzzle

Thanks to Robin for the suggestion! Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to learn how to make videos. Be prepared–animation is time consuming […]

## Do Storks Deliver Babies? – Numberphile

Author and economist Tim Harford talking statistics – more from this interview at https://youtu.be/NOTN2FsdUHQ More video links & book stuff in full description below ↓↓↓ Buy Tim’s new book “How To Make The World Add Up” (SIGNED COPIES at no extra cost) from Maths Gear: http://bit.ly/World_Add_Up Tim Harford books on Amazon: https://amzn.to/3lbt2vt And Tim’s own […]

## Incredible Factorial Problem!

This was the hardest problem in the 2002-3 British Mathematical Olympiad. Thanks to Nahian for the suggestion! British Mathematical Olympiad 2002-2003 problem 5 https://bmos.ukmt.org.uk/home/bmo1-2003.pdf A Mathematical Olympiad Primer Paperback – 1 Aug. 2011 Math Forum post http://mathforum.org/library/drmath/view/77092.html Math StackExchange post https://math.stackexchange.com/questions/2123011/find-all-positive-integers-a-b-c-to-the-equation-ab-abc Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas […]

## The Brussels Choice – Numberphile

Neil Sloane from the OEIS discusses the Choix de Bruxelles. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Neil Sloane founded the runs the OEIS: https://oeis.org/ Brussels Choice on the OEIS: https://oeis.org/A323454 Neil Sloane playlist on Numberphile: http://bit.ly/Sloane_Numberphile Neil Sloane on the Numberphile […]

## Largest Cone Puzzle

What is the largest cone you can make from a circular sector of radius 1? I thank Joe for suggesting the problem! Maximum volume of a cone shaped cup (KristaKingMath) Calculus 1: Max-Min Problems (23 of 30) Maximum Right Circular Cone Net of a cone (Geogebra) https://www.geogebra.org/m/KFzUmbgC#material/Vnm4PEtp https://www.geogebra.org/m/q9ud4ux8 https://www.geogebra.org/m/yzGzrUxs Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by […]

## 569936821221962380720 – Numberphile

A number of galactic proportions… See more #MegaFavNumbers on this playlist – https://bit.ly/MegaFavNumbers – and read below to contribute your own. More links & stuff in full description below ↓↓↓ See our full collection of video on the sum of three cubes at: http://bit.ly/SumOfCubes (*) the cube (which we depicted quite loosely and artistically, of […]

## A Clever Solution

Learn one weird trick to solve this problem! Thanks to Nestor Abad for alerting me of a typo in an earlier version of the video. Reference https://socratic.org/questions/if-x-sqrt-x-2-1-y-sqrt-y-2-1-1-what-is-x-y Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my […]

## Squares and Tilings – Numberphile

With 2006 Fields Medallist Andrei Okounkov More links & stuff in full description below ↓↓↓ Professor Okounkov website: http://www.math.columbia.edu/~okounkov/ Numberphile Field Medallist Playlist: https://bit.ly/Fields_Playlist Roger Penrose on the Numberphile Podcast: https://youtu.be/JiDWGbsVEno Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to […]

## The Wedged Angle

Can you solve this geometry puzzle? Thanks to Robson for the suggestion! Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to learn how to make […]

## Best Meeting Spot For 4 Friends

Which point is “closest” to 4 friends? Thanks to Chanul for suggesting this problem, which is adapted from a Sri Lankan Olympiad question. Special thanks this month to: Michael Anvari, Kyle. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions References Geometric median https://en.wikipedia.org/wiki/Geometric_median Plastria, Frank. (2006). Four-point Fermat location problems revisited. New proofs and extensions of […]

## Only 10 Percent of Students Solved This

Can you solve this problem that stumped many advanced math students? References https://io9.gizmodo.com/ready-this-simple-puzzle-once-stumped-96-of-americas-1698814691 https://www.theguardian.com/science/2017/jun/05/did-you-solve-it-are-you-in-the-smartest-10-per-cent https://www.mapleprimes.com/posts/206713-Puzzle-Or-A-Simple-Exercise http://puzzles.nigelcoldwell.co.uk/seventytwo.htm https://timss.bc.edu/timss1995i/TIMSSPDF/C_full.pdf Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube […]

## Dungeon Numbers – Numberphile

Featuring Neil Sloane from the OEIS. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor)… More links & stuff in full description below ↓↓↓ Part 2: https://youtu.be/HFeKdMf01rQ Neil Sloane is the founder of the The On-Line Encyclopedia of Integer Sequences. Visit it here: https://oeis.org More Neil Sloane on Numberphile: http://bit.ly/Sloane_Numberphile Numberphile is supported […]

## The Stacked Cubes Puzzle

This is a fun one! Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to learn how to make videos. Be prepared–animation is time consuming and […]

## The Folded Square Puzzle

I thank Ankit and Amlan for the suggestion! This problem is adapted from an examination at the prestigious Chennai Mathematical Institute. Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation […]

## Can You Solve The 6 Cards Game?

It takes perfect logical reasoning to solve this puzzle. I thank Joe for the suggestion! Reference to TED-Ed talk by Maurice Ashley Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for […]

## The Last Side Puzzle

This was given to 9th and 10th grade students in a math competition. Can you figure it out? References Question 23 of Kangaroo competition https://www.matematica.pt/en/docs/kangaroo/enunciados/2017/2017_Junior.pdf Orthodiagonal quadrilateral https://en.wikipedia.org/wiki/Orthodiagonal_quadrilateral Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare […]

## Hat Problems – Numberphile

Featuring Joe Buhler. See part 2 of this interview: https://youtu.be/4YG4QnhVV7A More links & stuff in full description below ↓↓↓ An Introduction to Infinite Hat Problems (paper): https://bit.ly/31OeWZK See also Spheres and Code Words with James Grime: https://youtu.be/T46FTuHnbvY Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, […]

## The Unfolded Box Puzzle

This is a tricky but fun geometry problem! Special thanks this month to: Michael Anvari, Kyle. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Adapted from Math Kangaroo paper problem 22 https://www.mathkangaroo.in/media/pdf/16556_Grade_8_Math_Kangaroo_Sample_Paper_-2019.pdf STEM4all video Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I […]

## Magical Triangle – Think Outside The Box!

Many people requested this one. It was asked to 9th grade students in India who had only learned geometry, so you are supposed to solve it without using trigonometry. I thank Anand Gautam for discovering the incredible solution! You can also solve the problem with trigonometry. This post does so for the 2nd part of […]

## For The Benefit Of Mr. Kite’s Midpoint

Thanks to Neelesh for the suggestion! This problem is adapted from the JEE Mains test in India. References https://doubtnut.com/question-answer/let-a-b-is-the-midpoint-of-the-chord-ab-of-the-circle-x2-y2-r2-the-tangents-at-a-and-b-meet-at-c-the-59570 https://doubtnut.com/question-answer/ab-is-a-chord-of-the-circle-x2-y225-the-tangents-of-a-and-b-intersect-at-c-if-2-3-is-the-mid-point-o-1158415 Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software […]

## A Circle With 4 Squares

This is a neat problem! Puzzle adapted from Cshearer41 What’s the area of the circle? pic.twitter.com/PkNRay2ysR — Catriona Shearer (@Cshearer41) April 6, 2020 Solve for the radius – harder than it looks Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use […]

## Beautiful Trigonometry – Numberphile

Featuring Ben Sparks. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Ben’s website: https://www.bensparks.co.uk More Numberphile videos with Ben Sparks: http://bit.ly/Sparks_Playlist Explore this topic further with this Geogebra file from Ben: https://www.geogebra.org/m/S2W46Thv Catch Ben on the latest Numberphile Podcast: https://youtu.be/-tGni9ObJWk More podcast episodes: […]

## Surprisingly Hard Angle Problem

Many people asked me to solve this one! What is the value of x? Many more solutions Can anyone solve this? I have a numerical answer using trigonometry. I did find a geometry "proof" online but it was faulty. Many people are requesting this problem, so I would like to make a video. Help is […]

## The Cornered Circle Puzzle

Thanks to Manoj and Katlego for the suggestion! Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to learn how to make videos. Be prepared–animation is […]

## Ladder And Box Puzzle

Special thanks this month to: Michael Anvari, Kyle. Thanks to all supporters on Patreon! A ladder leans against a wall, just touching the corner of a cubical box. If the ladder has a length of 4, and the box has a side of 1, what is the distance between the top of the box and […]

## A Surprising Pi and 5 – Numberphile

Ben Sparks discusses 5 and Pi. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Ben’s website: https://www.bensparks.co.uk More Numberphile videos with Ben Sparks: http://bit.ly/Sparks_Playlist Catch Ben on the latest Numberphile Podcast: https://youtu.be/-tGni9ObJWk More podcast episodes: http://bit.ly/numberphile_podcast Numberphile is supported by the Mathematical Sciences […]

## The Folded Semicircle Puzzle

This problem is adapted from a Belgian Olympiad. I thank Jente for the suggestion! Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to learn how […]

## Insanely Hard Problem – Solve For The Angle

I admit I didn’t solve this one! Sources https://www.duckware.com/tech/worldshardesteasygeometryproblem.html https://www.cut-the-knot.org/triangle/80-80-20/IndexTo60-70.shtml Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to learn how to make videos. Be […]

## The Square Inside The Square

Many people asked me to solve this one! And you know which theorem will come in handy to solve it 😉 References https://math.stackexchange.com/questions/2518341/area-of-a-square-inside-a-square-created-by-connecting-point-opposite-midpoint Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search […]

## Matrix Factorization – Numberphile

Featuring Professor David Eisenbud, director of the Mathematical Sciences Research Institute (MSRI). More links & stuff in full description below ↓↓↓ More videos with Professor Eisenbud: http://bit.ly/Eisenbud_Videos More form the Professor on our podcast: https://youtu.be/9y1BGvnTyQA The 17-gon: https://youtu.be/87uo2TPrsl8 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science […]

## Incredible Cube Puzzle

Thanks to Kieran in New Zealand for suggesting this problem! A version of this problem was given to 14 year old students in Taiwan. Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can […]