5 More Mind Bending Mathematical Mysteries
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- čas přidán 9. 06. 2024
- Embark on a journey through unsolved mathematical mysteries! Explore the Magic Square of Squares, Sums of Three Cubes, Hadwiger-Nelson Problem, Moving Sofa Problem, and the elusive Odd Perfect Numbers conundrum. Will these age-old puzzles ever be solved?
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It's a test from the Lizard Overlords to find the ones that need to be eliminated first. Allegedly. Cheers
That's conspiracy and not allowed on youtube bigot
😊😊😊😊😊😊😊
😊😊😊
😊
Give me that power
I only scrolled the first bit of comments, but I'm very disappointed that I didn't see any math knowledgeable person point out that Euler is pronounced "oi-ler" (i'll ignore how he pronounced the first name). The man is the greatest mathematician in history, put some respect on his name! ;)
Yep!
The sofa problem reminds of something I read in book. A guy and a friend get a sofa stuck halfway up a stairwell and keeps running simulations to figure out how it happened , instead of taking an axe to it.
It eventually turns out that a time machine materialized with its door opening onto the landing as the moving men were trying to get around the corner on the stairs. The owner of the time machine helpfully opened the door to help them turn the couch but had to leave quickly and dematerialized the door and the couch couldn't be moved forward or backward from the position it was in.
If you feel like you haven't been confused in a while, don't worry, Simon's got your back. My brain was glitching throughout the entire video.
I just can't follow and really comprehend anything he's saying as he talks way too fast. Have you ever moved your eyes back and forth really fast? Yeah... That's how I feel the speed of his voice is haha. Sucks, bc I'm really liking the channel.
What's confusing?
I can't even balance my checkbook and you hit me with this?
Cleary Simon hasn’t met a person like my husband, who took math classes for fun at university and received a math minor without planning to. He ws a History major.
Now I really want someone to make an actual Hammersley sofa with a removable half-circle section for the ultimate in nerd decor.
It's nice to hear Simon talk to Peter in videos other than the Business Blaze episodes. Sorry, I meant Brain Blaze, not Business Blaze (he should have never changed the name!)
I wish they kept it with the business idea but it is a brain blaze. ❤
Who is this "Peter" anyway? I've heard him mentioned many times in brain blaze, but also in Simon's other channels from time to time.
@@shupbender5487 Peter is his fake office plant
@@shupbender5487 I believe he's the editor?
@@shupbender5487 Peter is an extremely bigoted figment of Simon's imagination (and also his potted plant)
Douglas Adams used the sofa problem as a running gag in Dirk Gently’s Holistic Detective Agency
You can do it, Peter!
At 2:45 the squares shown are not magic squares of squares.
The Square Root of each cell entry in one such square is:
68,29,41,37
17,31,79,32
59,28,23,61
11,77,8,49
Square each cell entry and add them up.
The sums are 8515.
"I'll stick to philosophy, no math here"
*Reads The Meno*
"Plato, stop!"
That said, Simon I'd love for you to cover philosophical problems such as the Gettier Problem.
3500x3500 would be one insane Sudoku!
2:10
I enjoyed this bouquet of open math problems a bunch.
btw, sometimes spoken of as "4 modulo 9" or "13 is congruent to 4 mod 9", means 13 is a multiple of 9 plus 4, in symbols, 13 = (1 times 9) + 4 :) For this sort of thing, only whole numbers are used, no fractions allowed.
the graphic is a bit misleading. The result of 13 mod 9 is 4 is not because the fraction is a bunch of 4s. its because the reminder is 4.
I had a bit of a problem with their representation as well. Quite misleading.
Isn't the Swiss mathematician's name pronounced like Oiler?
I'm Swiss and yes, it is 👍😉
That's certainly how my university professors pronounced it.
I think I’ve heard Simon pronounce it correctly in other videos he’s done.
Yeah, only one of the most influential mathematicians ever (along with others like Gauss) and he screws up the pronunciation 😱.
1:20 - Chapter 1 - The magic square of squares
3:50 - Chapter 2 - Sums of 3 cubes
6:45 - Chapter 3 - The hadwiger neslon problem
10:00 - Chapter 4 - The moving sofa problem
Very enjoyable video. I really enjoy math and puzzle solving, though I'm not too good at either, especially some of them on CZcams. I did study calculus many years ago. I'm really not too bad at math. 😊
1:12 the magic square of squares
3:46 sums of three cubes
6:43 the Hadwiger-Nelson problem
9:55 the moving sofa problem
i dont understand the first one. The numbers are supposed to be squares: 1^2, 2^2, 3^2 so why are there in 4x4 square such numbers as 11, 7 or 3?
Because it starts of talking about just a normal magic square, not magic square of squares. So, instead of showing the square of squares, they seemed to just chose a normal magic square.
@@pandabytes4991 The 5th mystery is "where is the 5th mystery".
The missing 5th problem is about Odd Perfect Numbers. A number is perfect if it equals the sum of all its divisors (including 1 but not including itself). For example, 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14. All known perfect numbers are even. The unanswered question is, does there exist an odd number that is perfect? This is one of the oldest unsolved problems in mathematics.
It's interesting/weird to hear Simon pick on "Peter" when the character was created on a completely different channel of his (Business Blaze, now Brain Blaze)
It's just a little bit of Simon's real personality showing through on his serious channels. I'm all for it!
God I love this channel it makes my brain grow! Thanks Simon
Euler is pronounced "Oiler" btw.
Good ol' Lenny gave us so much - including a tricky name.
Paused the video to see if the parker square had been mentioned. It had not, so now it has.
Likewise!
You're an amazing speaker, love your videos! By your comments you do not dabble in math nor software programming often... I am curious to see the script you were reading during this video... I am in software and absolutely hate talking in front of a camera.... How do you do what you do? What is the script that you practiced, what were you reading while filming this? I am so happy to be a subsciber, and looking to support you more, you are so worth it! Absolutely not a bribe... whether you show the script or not does not determine whether I will or will not I become a patreon... ;-)
@2:28 The one thing I remember from linear algebra is that it's pronounced "OIL"er Not YOU-ler. Or maybe it was in Differntial Eq.
OMG love how you're doing a (recreational) maths video.
"Pivot! Pivot!" - Ross Geller
It goes to show just how much I like Fact Boi by watching this video…I don’t even like math!!
3:56 There's probably a word for this effect. My money is on "exponential".
5:55
So they finally found the question to the answer 42?!
I love how "Peter" as a meme has spread to almost all of Simon's channels! Lol
My name is indeed Peter and I really thought they have now found a way to adress any viewer by first name 😮 Glad to see Peter was just chosen by coincidence 🤔
No, it's not coincidence...Simon is kinda crazy. Peter is his fake plant, whom he often addresses in his Business Blaze videos
I mean his Brain Blaze videos. They used to be called Business Blaze
I'd love to troll you and say when I watched it he said Mark!
It didn't say Peter for me?!
Oh dammit! The whole foundation of my life has been destroyed. I was suitability impressed that Simon was able to address each viewer by name.
The solution of the 4-color problem was an interesting solution. It was the first problem that had all the options generated by a computer and then have the computer solve each one.
There was a lot of discussion as to whether this constituted a valid solution, but within time, it was determined it was a valid process.
the last one made me laugh. I tried to move an old couch into a spare room this weekend. def damaged the walls in my hallway a fair bit. the couch ended up being dismembered and thrown out anyway 😑
No headache today, until I watched this..
The moving sofa problem is easy to takle, you just have to yell "Pivot!" in anger.
5:15. The moment my brain started melting out my ears and drool
The magic square of squares lends itself to an interesting computer project. I spent a winter on this one. It turns out there are many things that do not work, so excluding them gets you very far, very fast.
My problem is I needed to write a 128-bit square root function based on 4 64-bit square root commands. It was spring, and I do outside projects, so I let this one go.
I used to drive myself mad trying to solve stuff like this when I was younger. Not quite the purely mathematical examples covered here but I remember my sister bringing home a puzzle from School to which she claimed there was a supposed solution - but 'conveniently' forgot what it was. Take a piece of paper. On it draw three squares. label them 1-3 and call them houses. Underneath, draw three more squares and label them Gas Water and Electric. The conundrum was to link up each house to Gas water and electric supplies by drawing lines between them. The puzzle was to do it in such a way that none of the lines crossed over. Sounded fairly simple in principle, but however you try, however you link up each of the supplies to each house (the lines don't have to be straight), it just can't be done. I don't believe there is an actual solution to it & the hours I wasted trying to achieve it - there's always at least one set of lines which cross! Thanks for an interesting video!
The solution is a spiral
The only way to solve that problem is to feed one of the houses through another one of the houses.
@@surferdude4487 Yes, I read that, but it was implied it was cheating when I first knew about it.
@@PoorlyHandled My sister said that (except conveniently didn't know exactly how to do it, just roughly) but try as I might I couldn't work it out! Gave up eventually!
@@jimmybisk LOL! A spyrol doesn't make any difference. There's probably some convoluted mathematical proof out there somewhere for this, but I'm sure as I can be that there is no solution for the three houses, three utilities problem.
Of all of Simon's videos this one is the most distressing; and i watch his Into the Shadows channel
It's OILER, not you-ler
(I find it funny that 42 was the last of numbers 0-100, considering how it's the answer to life, the universe, and everything.)
I find it hilarious that the video is about math, but the title shows that someone can't count. The title says there are 5 math problems in the video, but the video ends after 4 math problems.
6:08 you repeat some numbers here
4:10 Sound like the mathematical equivalent of “60% of the time it works every time”! 😂
Thanks for the headache Simon!
Not surprised there's maths puzzles that people are struggling to prove. I hated maths at school so the whole lots a puzzle to me😂 . Interesting video by the way
The Simon Whistler and Brady Haran universes are colliding
Here is a mind bender -> instead of counting in base 10, base 8, base 16, or similar; implement counting in base pi or some other irregular number.
It's not unfounded that less intelligent people, find solutions on subjects like these. When you know too much, you tend to overanalyze problems. Children for example have a much easier time solving logical problems than adults, because their minds are simpler. They just look at the basics of a problem. Even school curriculum have changed over the years, especially in math classes. No longer about solving the problem itself, but documenting how they came to the conclusion of the answer. Not surprisingly, most adults can't do children's match class curriculum because of this. We grew up going to school to solve problems, creating equations to find the answer. In math, equations were how we her trained to do math, but not for children.
We got a 3m^2 sofa in. Just took the window out of the frame.
It’s really eerie when Simon calls out your name. Twice.
Youve just got to shout pivot to easily move furniture
the Hadwiger-Nelson problem is more complicated and also simpler than it is portrayed... in its simplest form, 2 colors would suffice, but that assumes one can return directly to a tile of the plane that they had just left. Baring the ability to simply return to a previous tile without first moving to a 3rd tile, the answer becomes 3. However, this becomes ever more complicated as you add additional adjacencies to the plane. As a result, the number of required colors increases with each new adjacency. In example where-in the answer is 3 there exists only 2 adjacencies. In the solution with 7 colors using a hexagonal grid, each tile has 6 adjacencies. Ultimately the answer to this problem really is far simpler than it has been made out to be, the answer is simply 1+the total number of adjacencies for any given tile in your planar grid. It isn't an unsolved mathematical mystery, the solution has been known for quite a long time. In fact, the solution was a necessity for functional networks using routers and switches, the internet you are using right this moment would not function the way it does now without a solution to that very problem.
Is this a ChatGPT-generated comment? Anyone who understands the Hadwiger-Nelson problem can see that this paragraph is nonsensical.
@@JohnDoe-ti2np No it was not a ChatGPT-generated comment. And I do very much understand the problem. The actual problem has been blown out of proportion by peoples desire for it to have a simple clean answer with a single value, but the reality is that no single value can actually work. Even if someone were to create a proof to claim that the answer is a specific number, someone else will inevitably come along with a proof that shows the number they claimed it to be doesn't actually work. Different simple geometric shapes arn't even the only thing that changes the resulting answer, abnormal shapes do as well. You could have a grid made up of Isosceles triangles and require more than 4 colors all depending on the exact angles of those triangles and if one considers corner to corner to be touching or not.
@@RaighnRPG ChatGPT-generated at not, what you're saying is nonsense. Not that I'm trying to convince you, of course, but other readers might be confused and think they're stupid for not understanding what you're saying.
Best yet.
The moving sofa..
the smallest distance from the walls is 45 degrees and that's the max distance to work with.
Therefore the length of the shape from end to end must be width of the hallway, 'x', times radical two, twice.
Therefore its 2x\/2, where again, 'x' is the width of the hallway
Knowing this, you can now come up with a shape for the sofa within that criteria to maximize the area.
Thoroughly enjoyed this video. But I wonder what the actual number of complete views will be.
Everyone named Peter who is not in on the joke is probably confused af for being called out.
05:52 - Could Einstein figure that out?- 😂😂
Jeez, rocket science in sight!
Please do a video on the UK dowding coastal radar system used in ww2
Stand the sofa up when it's end. And that way the sofa can be as long as the hallway is tall.
My name is Peter... No, I probably couldn't solve any of these if my life depended on it. It was trippy hearing you call out my name specifically though. I appreciate the vote of confidence. 😁
POV: Your name is Peter, and you're eating dinner when all of a sudden Fact Boy yells out your name... Wild.
1:40 - Unique, that is, unless you're Matt Parker.
Breaking that 4th wall for Peter.
Shout-out to all the Peters watching this!
Ok ...
Thanks 👍😉
Quick question: If you can construct a proof for the map-coloring problem, I guess you have to consider "all" possible maps. Is it really that much harder to construct "all" possible shapes of sofas?
Solution to the Sofa: place the sofa, build the room around it.
I have a solution to the last one...make bigger hallways.
2:45 those are clearly not the magic squares in question
4:37 that's not the remainder, that's the period (for 9 they match, but still)
Oh MY, you've trapped me; I love puzzles and had a bit of mathematics shoved into my brain over the years. I *should* be taking my afternoon nap now, you "terrorist", or whatever the title should be. "torturer"? Torturer seems to fit better, how 'bout Sadist? I also tend to get trapped into doing multiple episodes of your more mundane stuff: Just ONE more?", my poor brain pleads, and the body says "no", and I get some more nap time, as needed.
nice studio!
Chance that Simon understood any of this: 0%
As many times as I hear you explain it, I wish I were smart enough to understand the Monty Hall problem one. I just don't get it. I'd probably go home with a mule-cart load of baked beans. And I got an "A" in statistics in college! That was just so long ago... Hugs
That's not a mystery though, since it's "solved", or more precisely it was never a problem.
Just draw up all the possible starting positions (there are three of them), then do all possible selections, then look at the options after that. It'll become quite clear after that.
You'll also find that the three starting positions and the three choices are quite symmetric, so you'll get back to 3 options, making the whole thing simpler than at first glance.
@@ciCCapROSTi My brain is somehow stuck on equal probability syndrome. I read the wiki, but my brain still refuses to believe anything other than 50/50. I'm caught in a facile loop. Thank you, though. Hugs
The only think I can offer is the one thing that I needed to know. The exposed door will ALWAYS show a "bad" prize, not the grand prize. Knowing that means that it's no longer a 50/50 thing.
Nice one Kevin ❤
I think Euler is pronounced oy-ler (rhymes with boy).
The biggest Mathematical Mystery is the Hubris to expect that the Universe is defineable by using Math based on 10!
no-one's ever called me Peter before
But did you know that it is mathematically proven that you can turn a four legged table that has wobbly legs until it doesn't wobble?
You would think that whole.magic square thing would be simple enough. Basically you would take the first 1-9 example (odd numbers top bottom left right, even numbers in the corner) and use that as a template for a 3 by 3 square of squares.
Actually, your explanation of the whole sum of three cubes thing might hide the answer to why you cannot make this magic cube of cubes. Idk why but my gut is saying the answer is there.
Who else thought the 5th mystery would be optimal square packing?
I first head of Recreational Mathematics on an episode of Doctor Who.
It's Sci-Fi. Doing math for fun is Science Fiction.
Magic Cube…. 114 would be each lines sum, who do I call for my money?
Is the fifth math mystery trying to figure out where the fifth math mystery is in the video?
I have a thick book of sudoku almost completed with exception to the very hardest last section. Also did I just hear the sound to tetris playing in the background ? Haven't heard it in years so not so sure about that sound.
4... FOUR more mind bending mathematical mysteries! I feel cheated
Whoops! 2:27... that is not how you pronounce Euler (a pedant writes).
Once again, the cabal makes an easy concept sound impossible.
Tricky maths problems are tight.
Nice. Euler's name is pronounced "Oiler," though.
(Speaking of numbers, my "like" was #666!)
Number three: The Hadwiger-Nelson Problem
Is this not solved on a 3 dimensional plane?
I wonder how many people named Peter clicked on this video not knowing Simon's go-to generic name is "Peter"
I could feel my eyes glaze over trying to follow this video.. thoroughly confused
The 5th mystery is how you can make 5 mysteries out of only 4.
The big mistary here is how did you know my name is Peter. :D
Do it Peter. Do it.
Pretty good video, but none of these were close to paradoxes, like the thumbnail said they were.
And the reward to the video that made me have the smoothest brain by the end goes to....
Moving sofa problem - don't ask Ross 😂
I'm getting a headache just watching this. Lol
Diagrams/ illustrations 🥳🥳🥳
There are a large number of apparently simple problems that we don't know the answer to. For example, the twin prime conjecture states that there are infinitely many twin primes (primes which differ by 2 such as 17 and 19 or 41 and 43) but no one's been able to prove or disprove it yet. There's a simple proof that there are infinitely many primes, known at least as far back as the ancient Greeks when it was proved by Euclid, but an answer for twin primes still eludes us.
There's an infinite number of numbers so of course there is an infinite number of primes. And, I would assume, also twin primes.
@@gobblinal That doesn't necessarily follow. Primes get rarer as the size of your numbers increases, so it's possible they could just peter out altogether when your numbers get large enough. Alternatively, as your numbers increase there are more and more numbers which could be factors of them, so maybe above a certain point everything has at least one factor. You need a proper mathematical proof to show that this doesn't happen.
Similarly with twin primes; as primes get rarer with increasing size, maybe the minimum distance between them becomes 4, then 6, and so on.