Can you solve the Mondrian squares riddle? - Gordon Hamilton

Dutch artist Piet Mondrian’s abstract, rectangular paintings inspired mathematicians to create a two-fold challenge. Can you solve the puzzle and get to the lowest score possible? Gordon Hamilton shows how.

Lesson by Gordon Hamilton, directed by Anton Trofimov.

Thank you so much to our patrons for supporting us on Patreon! Without you this video would not be possible! Bozhidar Karaargirov, maxi kobi einy, Misaki Sato, Craig Sheldon, Andrew Bosco, Catherine Sverko, Nik Maier, Mark Morris, Tamás Drávai, Adi V, Peter Liu, Leora Allen, Hiroshi Uchiyama, Michal Salman, Julie Cummings-Debrot, Gilly, Ka-Hei Law, Maya Toll, Aleksandar Srbinovski, Ricardo Rendon Cepeda, Renhe Ji, Andrés Melo Gámez, Tim Leistikow, Moonlight, Shawar Khan, Chris, Megan Douglas, Barbara Smalley, Filip Dabrowski, Joe Giamartino, Clair Chen, Vik Nagjee, Karen Goepen-Wee, Della Palacios, Bryan Blankenburg, Bah Becerra, Stephanie Perozo, Marc Bilodeau, Ruby Solorzano, Ivan Tsenov, Claudia Mayfield, Justus Berberich, Pavel Zalevskiy, Yankai Liu, Duo Xu, Ghassan Alhazzaa, Miloš Stevanović, Joy Love Om, Gi Nam Lee, Shawn Quichocho, Simone Kidner, Anika Westburg, Barun Padhy, Brandy Jones, Devin Harris, Tony Trapuzzano, Stephen Michael Alvarez, Tom Lee, Juliana, Jason Weinstein, Kris Siverhus, Alexander Walls, Annamaria Szilagyi, and Morgan Williams.

[pauljk-]

"What should we do for the bonus riddle?"
"Lets take the riddle and just make it bigger"
*Brilliant*

[pjabrony]

Cover the entire canvas with a single 8x8 rectangle.


Largest rectangle: 64
Smallest rectangle: 64
Score: 0


I win.

[joshschilling]

I stopped at the “pause here” and basically spent 5 hours of my free time in the next 2 days trying to solve this and I finally got the best solution possible!! I was so proud of myself and I love this riddle and their riddles in general.

[micahgoldson]

“Can we do even better? No.”

Me: Oh thank goodness

[jules]

I know that I will not take the time to solve this, but I still watch it anyway!

[jules]

These riddles are my favourite type of Ted-ed videos, anyone else?

[BioHzrd]

Step 1: Confirm you have green eyes
Step 2: Ask the canvas to leave

[BhanuPChauhan]

With this kind of voice narration, this question feels like a matter of life and death.

[egyteguhrinaldiputra]

Anyone else always just watch these riddle videos till the end but never even try to resolve them ?

[CuriosityCulture]

I get anxiety from riddles.. Still great video Ted :)

[dominickeijzer]

Don't cut it. That's how you get the lowest score. Say it has an area of 8. That'd be the smallest and the largest, meaning your score is zero.

[abdulmasaiev]

"Cover a square with non-identical rectangles"

Uh... How about the entire square? Squares are rectangles, so that is one too. It's unique since there can't be two of the same if there's only one. Its sides are whole numbers. It covers the entire area. The score is 0, you can't go lower than that since MAX >= MIN, so MAX - MIN >= 0. It doesn't even matter what size we're supposed to cover (assuming it's whole by whole, which it has to be or you'd never cover the entire thing no matter what), we're done here.

[uriusartes]

I've never been feel so confused in my life

[thebros]

3:04
Is nobody gonna talk about the two rectangles with an area of 48 having the same dimensions?

[miloandash]

More riddles please I can't get enough of them! They're my favourite type of video you guys make.

[channelknightfadran]

Ted: *Goes into lots of math to determine smallest possible number*
Me: *Draws chart and gets 12-12 on the fourth try*

[noorkhudair]

I got 10 :'(.... lol at least i tried

[DeveloperTharun]

Being a web developer, every canvas reminds me of CSS Grid.

[slimeyslime]

I tried it, and I got a score of 2 on a 100x100 square

[jacksonhawkins]

What I did:
I wrote out the possible areas and ordered them. Then I tried to make 64 using various combinations. Through desperation and figuring out the "odd rule" mentioned in the video's solution, I came across the 8-8-10-12-12-14 combo. It fit in fine, but I still felt like there was a better solution. I tried for quite a while after that, but I didn't even find the second solution in the video. In the end, I felt I had failed, and even when the answer came up in the video, I feel more like I lucked out than figured out.