A Problem with Rectangles - Numberphile

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NUMBERPHILE

Videos by Brady Haran

[uplink-on-yt]

I got into Oxford using this test, but the second security guard wasn't as impressed as the first and kicked me out.

[YouennF]

The math and fun content of this is high, but must not hide in our minds the quality of the "off-brown paper" animations presented in this video !

[AlanKey]

I'd love to hear how the Oxford applicants responded to this question.

What was the neatest solution Tom Crawford saw from a student?
What was the weirdest solution?
Did students make embarrassing / common mistakes?
What sort of fraction of applicants got the full answer?

[LewisDruid]

Quite off-topic, but I think it is neat to see this guy working at Oxford. I would assume such a prestigious uni would be very picky about how it's faculty and staff appear, but they let him be there just fine with his piercings and tattoos which is wonderful :D

[fomx]

Very cool. I like that this is the kind of problem they ask candidates for uni.

[Zarunias]

I tried the 7 rectangles on my own and came up with a completely different solution with one 2/5x4/5 rectangle, two 3/10x3/5 rectangles and four 1/5x2/5 rectangles.

[TuberTugger]

I paused the video for the 7 solution and when I did it myself, I got a different answer.

It still involves 3 different sized rectangles with a single largest one. But the large one is smaller and has one of the smallest rectangles to finish it off.

Instead of fractions, I worked with a 10x10 square for easier math.

You need:
1x 4 by 8 rectangle
4x 4 by 2 rectangles
2x 3 by 6 rectangles

One half of the square is a total of 4 by 10 (4 by 8 + a 4 by 2)
The other half is a total of 6 b 10 (all remaining rectangles) => the 3 by 6s form a 6 by 6 square and the 4 by 2s form a 4 by 6 square.

Just in case anyone was curious. It is a unique solution because the number of sized rectangles is different than Tom's.

[Verlisify]

I like to imagine Mathematicians from centuries ago being comparably as exciting and quirky as this guy is to us today

[dylanwinestone]

Me feeling vaguely smart for seeing the n+3 method and n+4 method from the start, but then realising I hadn't come up with the building up

[mathoc]

Tom is great! I can see why you use him so much. Perfect numberphile guest. He clearly has FUN with math and I think thats part of what numberphile is all about.

[HarrisD]

This was surprisingly interesting. The solution was so clever.

[ASOUE]

What I love about numberphile. This is an excellent display of leaping induction without mentioning leaping induction.

[shikhanshu]

I didn’t expect much but the video kept me glued all the way to the end!

[Keepturbo]

I always found it curious how school managed to make me dislike math in the way it was presented/forced upon me in school. Only to re-discover a passion for math/physics in my own free time later on in life (albeit after completing a completely different educational path), partly due to all these great youtube channels. And i guess the point that i'm trying to make is that i am pretty thankful for that.

[OrangeC]

This guy has an anime hairdo, and now I want to see an anime where the main character is a mathematician

[dannybodros]

Cloud Strife retired as a mathematician after defeating Sephiroth.

[freerkderuiter]

For some reason I’m thinking of tatami mats right now.

[Hackfresse]

This is a really cool puzzle. Now I'm wondering what the solution is for other ratios.

[jrjihu]

I got a different solution for the 7 rectangle problem. I started off by marking an 8 by 8 grid. I started with two 6 by 3 rectangles next to each other creating a 6 by 6 square in one corner of the large square. Then on one side add two 2 by 4 rectangles, leaving only a 2 by 6 area empty. Then I added another 4 by 2 rectangle leaving a 2 by 2 area empty. Finish it off by splitting that final square into 2. So in the end I have two 3 by 6 rectangles, three 2 by 4 rectangles and two 1 by 2 rectangles.

I wonder how many solutions there are for each size.

[sebastianelytron]

The Bermuda Triangle used to be known as the Bermuda Rectangle,





until one of the sides mysteriously vanished.