90% of the world's top students did not solve this simple problem

Can you solve this problem that stumped many advanced math students?
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[@mikekalish6796]

I'm 76 and it's been 54 years since I got my engineering degree. I solved this in my head (with a little help from Pythagoras) in just a couple minutes......and it made me feel awesome that I "still got it". :-)

[@degenerationz9284]

Very nice :)

[@GordieGii]

I'm 59 and it's been 41 years since I graduated from high-school. It took me longer to figure out how long since I was in high school than the four 3-4-5 triangles. About 20 seconds for the string. 30 for subtraction. You still rock. Using Pythagoras I would have needed a calculator. (well, not 'needed' but I probably would have used one and taken longer than you.)

[@varsheshpatel6396]

Hey I did it in 5sec it's easy if you unroll the cylinder into rect and yeah Pythagoras is the last step

[@mikekalish6796]

@@varsheshpatel6396 When I "unrolled" the cylinder in my mind, I didn't get a rectangle.

[@crimsonram6106]

I'm sitting next to my baby in the morning and shaped her blanket to understand how the questioned line goes, then 3 4 5 that I still remember 😊 I lost the chance to solve it based on the first solution but got the second 😛

[@smylesg]

You _know_ those 90% tried the calculus way and just ran out of time.

[@sunchess5950]

Unwrapping is the best visualisation way to solve this

[@itsadityagupta2110]

But i didnt😂🔥🔥🔥🔥🔥🔥🔥

[@nihiIego]

Then they’re not good enough do do the second solution lol.

[@wernerviehhauser94]

Thats exactly the calculus problem (its even in the NAME calculus, you calculate using rules you know work but do not understand). They know how to do it, but they have no concept of why to do it in this or that way. Therefore, they lack the capability of visualizing a problem in a different way. Just take the 4 points on a sphere problem - calculus works and takes ages, visualized in a different way it boils down to doing 3 coin flips.

[@lucasa.8223]

This is so true! I did this using the calculus method, but couldn't remember the formula for the length and had to derive it at the spot. I could definitely see myself running out of time during an exam!

[@user-rv9vk8by5i]

Or, even easier, To go from left to right, the string has to stretch 12 units horizontally To wrap around 4 times, it must stretch 16 units vertically Thus, √(16²+12²) It's basically equivalent to the second method, but without unrolling the cylinder I was seriously confused when I solved it in under a minute and skipped forward to see integrals

[@ruairigarrett6834]

a nice way to see this is to imagine cutting along the string - then you can clearly see the right triangle

[@bruhman1845]

The same thing I did. Idk why people make it complicated when it’s that simple

[@deucedeuce1572]

Very simple. Same here. Was a simple, perfect grade school 3,4,5 triangle too, so no real math required either.

[@giantpunda2911]

@@ruairigarrett6834 I did it this way too. It's pretty much a variant of the simple trick version shown in the video. Rather than solving for 4 small triangles, you solve for one large right triangle with the spiral being the diagonal.

[@SaturnusDK]

There's actually a formula for this problem which is occasionally used in electrical engineering; l=(L^2+(NC)^2)^0.5, where l is string length, L is the rod length, N is number of turns, and C is circumference. Basically exactly the same as your solution just that it works for any rod length, any number of turns, and any circumference.

[@Zetds]

I imagined this in my head as the string that unravels into a hypotenuse of a triangle with the base equal to the rod's length (12) and the height equal to the number of winding times the circumference (4x4 = 16). Solving using Pythagoras gave 20 as the answer. Feels good to occasionally be able to solve a problem given from your videos :D

[@WhirlwindCK]

This is also the solution I first saw; thinking of the string as the hypotenuse of one 12x16 triangle rather than splitting it up into 4 separate 3x4 triangles.

[@roxaskobold5101]

Same here! Cheers!!

[@theMuritz]

Exactly my take, just unwrap it into a single triangle ….

[@joegrey9807]

Ditto.

[@deucedeuce1572]

Was a simple, perfect grade school 3,4,5 triangle too.

[@Z3r0XoL]

moral of the story: its always simpler when theres no circles involved

[@thetimebinder]

Except when it's more simple when you make it a circle.

[@kned7288]

I agree, Circles make a topic much more complicated, like rotational motion

[@Beebo]

I only solved this because I learnt the technique of flattening 3D shapes from the Hard Korean SAT video where the solution involved flattening out a cone into its net.

[@kavinc710]

Mind sharing that video?

[@Beebo]

@@kavinc710 kzbin.info/www/bejne/j2fGkoSVbcSZqLc

[@kavinc710]

@@Beebo Thanks for that... And another point I am also a follower of your channel!!!

[@Keldor314]

Yup, I remembered that one too and instantly knew how to solve this. This one is easier since it's more immediately obvious that unrolling a cylinder preserves length. Also the other one had that sneaky bit about counting just the portion that was going uphill that I totally overlooked.

[@hippophile]

Nice. 50 years ago as young kids we used to actually make some models (cubes, cones etc) with paper and glue, so the method would have been obvious from the physical experience! Back when everything wasn't digital and exams were not so starkly the main endpoint of education... :))

[@lbsgaming1982]

When you showed the calculus method first I thought there was no way my method was right, but the second method you showed was exactly what I did! Made me feel good about myself, thank you.

[@SuperTubbyTube]

I did this in about 30 seconds in my head while driving to work at 5:30 am. I recognized the 3-4-5 triangle and multiplied by 4. I’m surprised that only 10% of advanced math students got this. Cool calculus version; i wouldn’t have thought to set it up that way.

[@faellyss161]

overly trained to do calcul they forgot to use their brain efficiently and how to think differently, it's easier for untrained people with a flexible mind like you (i suppose) or me or many here

[@farrasalharits5966]

Yeah, me too! Maybe the test is full of calculus question that the student just autopilot to solve it with calculus

[@b.a.7586]

Ugh, i did it in 5 seconds at 3:30 am while i was drunk,stoned and sleeping. Get your game together mate

[@pixel5341]

I solved this without even thinking while I was sniffing a line of coke off my dogs back as I was walking her all after two hard nights of partying with no sleep. Yall need to get your life together.

[@star_of_light]

that's not how you drive responsibly

[@Arob4343]

I used the trick immediately. Probably because watching you has trained me to look for simplified shortcuts

[@robsbros2]

Same lol

[@aa6eheia156]

@@robsbros2 same.. got the answer instantly

[@wckvn]

I used it as a second method. Spent 2 minutes of the first integral method just to realize that it is too long and I don't have it on top of my head... So, went to seek a trick... spent 1 minute on that and 1 minute to solve it.

[@zulupox]

Me too :)

[@merxbj]

Exactly. Didn't even think about it. Just immediately went unwrapping. Involving calculus didn't even cross my mind :-)

[@pepehimovic3135]

Visualize unwrapping the cylinder to make a triangle with a base of 16 and height of 12. The length of string will be the hypotenuse. Meaning, 16²+12²=(length of string)² We get 20.

[@sunchess5950]

Yes same approach of unwrapping because it's very easy approach with imagination 🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳

[@lucaacco9631]

Pythagorean triad gang

[@gualtieromalpezzi2458]

20

[@darkhoodchief]

I got it using that approach

[@souhardyamalakar6951]

That is exactly what i did...👍

[@AeroLowdown]

One of the very few of these puzzle that I was able to get right before watching your (as always!) fantastic walkthroughs

[@scottyp1722]

I solved it by imagining the cylinder being rolled on a table leaving the string behind as it went. The distance that the cylinder would roll would be 16 (4x4) and the distance the string would extend from beginning to end would be 12 (the length of the rod). The string now forms the hypotenuse of a triangle with sides 16x12 and would be 20.

[@SaturnusDK]

There's actually a formula for this problem which is occasionally used in electrical engineering; l=(L^2+(NC)^2)^0.5, where l is string length, L is the rod length, N is number of turns, and C is circumference. Basically exactly the same as your solution just that it works for any rod length, any number of turns, and any circumference.

[@Mauro-82]

I did the same

[@stephen7630]

The great thing about this method is that a triangle with sides 12 and 16 is obviously a 3,4,5 triangle, so you don't even really need a calculator or even paper since you don't have to square the 16 and 12.

[@hannibal8810]

@@stephen7630 i didnt realize it was a 345 and did it in my head anyways lol

[@seraphina985]

@@SaturnusDK More generally it is the length of the turn as it applies to shapes other than a cylinder which is useful since you will often be wrapping wire coils around other shapes. Transformer cores tend to be a hollow cuboid with the wiring wrapped around two opposing sides for example.

[@johnhumberstone9674]

I just KNEW Gougu would make yet another appearance here at some point...

[@eternity44]

lol

[@UnimatrixOne]

and therefore - thumb down!

[@TAT4guitar]

It caught me So off guard when he said it x) Biggest plot twist sice GoT 1x09

[@JohnLeePettimoreIII]

😄😄😄😄😄😄😄😄😄😄 😄😄😄😄😄😄😄😄😄😄

[@abryg8655]

The nickname of Pythagoras was Gougu ?

[@MikePhoenix007]

This was actually very easy; did it in uber 30 secs in my head. 90% advance math students got it wrong probably because they weren't expecting this easy a question really and got trapped overthinking. It happens. Being used to difficult problems sometimes makes you blind to simple solutions.

[@nothingspecial9370]

Yup what you said happens a lot

[@anthonylosego]

The easy wrong answer is to take 4 x 4 plus the length... 28. But this does not account for the diagonal just the vector components. It would be half the perimeter of the rectangle from the diagonal.

I think the problem is that most students only have theoretical knowledge. They know how a lot of things in theory works, but knowledge is only useful when one has learned how to apply it into the real world. A cylinder is just a rolled up sheet of paper. But if one only works theoretical, which most students do, they may lack this connection.

[@xuklysc]

@@anthonylosego I did it the second way and failed because I really didn't expect the problem to give the circumference so I assumed 4 was the radius. I really wonder how many of them failed that way

[@PerfectHandProductions]

LOL Get good. I did it 1 second.

[@johncochran8497]

Used a similar method to the number 2 solution. Imagined rolling the tube and letting the string mark the surface, creating a triangle. Had to roll 4 times, so one leg of the triangle is 4*4 = 16. The tube is 12 inches long, so that's the 2nd leg. And 20 = sqrt(12^2+16^2).

[@dioptre]

I did the same :D

[@mehg8407]

I had the calculus method picture in my head and the arc length formula ready for use. I knew there had to be an easier way. The flattening out trick was pretty cool, I must say.

[@cloroxbleach7554]

I went with the second solution using the *Pythagorean* theorem to find 4 similar 3-4-5 right triangles which gives us string length = 20

[@Mindhumble]

2:55 i did it slightly idfferently. i imagined the rod being stretched out as if it was a rectangular piece of paper which had been rolled up 4 "rolls", so by unraveling it 4 times you get a width of 4 times the circumference(of 4) giving you and 16x12 green rectangle with the string going from corner to corner, and using the 3,4,5 ration you get a 12,16,20 triangle---> 20!

[@aka5]

it is basically the same method

[@Mindhumble]

@@aka5 yes

[@noahniederklein8081]

Same

[@bluerizlagirl]

There are similar and congruent triangles lurking here! Each of the four turns is a distance of four around the rod and three along its length. You get four congruent triangles, one for each turn, which are similar to the four-turn triangle. But the actual maths is over so quickly, it's hard to analyse in much depth what you actually did ..... You probably used similar triangles with the 3-4-5 triple, even if you saw the whole journey as a 12-16-20 triangle and only realised that was the same as treating each turn separately on the way to the refrigerator for a post-maths treat!

[@Mindhumble]

@@bluerizlagirl i guess i saw the string as a sort of extender of the size of the triangle since i saw the angle of the string was constant. i hope that made sense.

[@igxniisan6996]

3:21, Deriving the ultimate formula for it: [√(c² + (h/n)²)]*n = [[√(n²c² + h²)]/n]*n = *√(n²c² + h²)* Therefore length of the string *L = √(n²c² + h²)* where n is the number of turns, c is the circumference of the cylinder, h is the height of it.

[@mikekalish6796]

This reminds me of a problem I solved a long time ago using calculus, only to find out there was a much simpler way. It was: Given a sphere with a 6" hole through it, what is the remaining volume? Of course the hole is cut through the center of the sphere such that the centerline of the cylindrical hole coincides with the diameter of the sphere.

[@ehsaanulhaque1857]

Plot twist: Gougu paid Presh to call the Pythagorean Theorem “Gougu”.

[@AbhinavKulshreshtha]

You might be right..😁

[@joostvanrens]

Plot twist Presh = SQR(2 * Gougu^2)

[@pushkard9377]

@@joostvanrens So presh is 1.414 times gougu? In which characteristic?

[@heldercomp]

I confess: it’s annoying. Look like social engineering.

[@germsbaegone1635]

heck no, that's what its called in Chinese "gougu"(勾股)JSYK

[@Spyx84]

Whenever I can solve one of these Bad Boys I feel like Einstein

[@sebastianescobar7182]

HAHAHA same here😂😂😂

[@Allangulon]

Depends on which way you solve it, the sheet metalworker in me did it the second way, it took about 30 seconds!

[@ErikBongers]

With every like this comment gets, I feel less and less Einstein.

[@aweebthatlovesmath4220]

You should feel like someone like reimann ... because they are mathematician not physicist.

[@Allangulon]

@@aweebthatlovesmath4220 Physicist.

[@UteChewb]

I thought about using calculus but figured there was probably an easier way, considering the shape could be broken into simple one loop modules. Then the unwound loops would turn into straight lines, giving a whole number of triangles ... and bang. Thanks, this gives nice insights into real world things like coils etc.

[@MaDaNi991]

I like that it took me 15 seconds to solve it in my head. Thanks to your videos that always inspire to think of shortest ways to solve a problem.

[@zackwhite6199]

The way I did it was by imagining unraveling the string although keeping it at the same angle that it was raveled around the tube at, then you have the hypotenuse of a triangle with sides of lengths 12 and 16, so I then used Pythagoras' theorem to work out the length of the hypotenuse, which is basically the second method.

[@jainab1522]

Come on now. The right triangle theorem has been found to be used as far back as ancient Babylon, hundreds of years before the Zhoubi Suanjing in which the Gougu Theorem was written written. If you do not want to allow Pythagoras to co-opt the name of the theorem because he was not it's originator, than you should also not ascribe the name Gougu to it either. As the identity of the person who originally discovered it it lost to ancient history, should you wish to be the most correct, both technically and politically, just call the the Right Triangle Theorem. You're a smart person, so apply some logic to the situation, and mind your decisions.

[@UnimatrixOne]

Right!! Gougu = thumbs down!

[@francescoduggento6981]

It's not that big a deal to be fair

[@bificommander]

He's been getting dozens of comments like this every time he mentions Gougu, and he hasn't stopped doing it yet. You're running into that definition of insanity thing.

[@jomama3465]

Tbh political correctness has no place in math lol

[@cigmorfil4101]

Call it the *BABYLONIAN THEOREM* Simples!

[@ucg-gaming]

I got this in a different way. The string wraps around the cylinder 4 times, so i "unwrapped" the string and that got me circumference (4) times by the times the string originally was wrapped around (4) so 4 times 4 which is 16 then i used Pythagoras to do √ ((16^2)+(12^2)) which gave me 20

[@norsanh3010]

After watching so many of your videos, I finally find one of the 'simple tricks' to solve the problem! Thanks, I love that I can progress watching videos!

[@Darrakk]

I solved this using Billy's theorem. You just need to substitute Michael's constant and run it through Brigit's function, and BOOM, Kelly's your aunt!

[@cigmorfil4101]

Kelly's your aunt...or Robert's your father's brother...

[@trueriver1950]

Billy's theorem: Are you referring to Mr William Pythagoras by any chance?

[@nickpro8116]

Presh, it might be wrong to call that theorem "Pythagorean", but this is the way this rule has been referred to by the mathematicians for centuries and this is already something we have all more or less agreed upon. There are lots of rules in maths which are not called after the ones who first discovered them, but we just know them under these names because we are used to, and that's okay. It is much like naming every single book you have in your house in the language of the person who wrote it. You might sound like a polyglot, but this will indeed cause difficulties understanding. In fact, this has already caused troubles understanding especially amongst those who are new to your channel. Even I, a person who watches your channel for a fairly long period of time, am always watching the comment section of every video featuring this theorem and I always see dozens, if not hundreds, of comments mocking the use of the term "Gougu" while speaking English. It has become highly annoying to hear this name for such a simple rule that everyone knows, and knows exactly under that name which you keep refusing to use. I do not understand why you are so intent that this theorem should be using its Chinese name. This might bring satisfaction to you, but I am pretty confident that to a vast majority of your viewers this has brought nothing other than confusion and annoyance. I know the world is unjust, but if trying to solve a problem you have only made it worse, this is not a logical thing to do. Maths isn't about "right" and "wrong" names, we just go for the ones that are generally accepted. Don't try to convince everyone this is a right name. This is like single handedly trying to change the grammar rules of a language. You can't do it, especially if it annoys everyone.

[@guptarishav50]

That was a pretty long comment. But worth the reading time. I agree forcing a new name is irrelevant for math formulas., 👍

[@mr.moodle8836]

Tbh I kinda like it, but only because his comment sections mocking it are more entertaining than all the "I'm 12 and I solved this in 5 seconds 😩" we used to get.

[@gabrielobando7761]

Well, the top two comments right now are about the Gougu theorem, add those to the other dozens of comments about it and you can see that it generates a lot of comments. I guess for a KZbinr, more comments=more popularity=more profits, so that may be why he insists on calling it that way?

[@chol-gd8zk]

nice

[@johnjordan3552]

You're new here aren't you. He hasn't changed his ways even after facing comments like this for years, he is not going to change

[@erikwynn9722]

There is a simpler way to solve this. Simply roll the cylinder 4 full rotations, unwinding the string. The cylinder will have travelled 16 units, and forms the hypotenuse of a right triangle with one side being 12 units and the other being 16. Using the Pythagorean formula you get that the length of the string is sqrt( 16^2 + 12^2), which is 20.

[@Arrogan28]

I learned along time ago in trick math questions that you are suppose to do without a calculator to remember the standard easy sides vs hypotenuse ratios, ie the most classic one being 3,4, and 5 for the diagonal, ie sqrt(4^2+3^2)=5 Others being 6-8-10, 9-12-15, but are rarely remembered by most people, so most times the problems use 3-4-5 right triangles. Something i find is common enough to be worth remembering. The trick is in this particular conceptualizing that the path of the string is similar to when you take a shortcut along the diagonal of a right triangle vs traveling the length of each of it's sides. I conceptualized it using 1 segment, and unwinding it rather then doing it all at once, but the math works to be the same. Most people think the answer will be just the circumference length around the rod times 4 for going around 4 times, plus the length of the rod. At least I once argued with my entire calculus study group around this idea. And they all thought you could just do that, ie in their minds the answer was 4 times around a 4 unit rod, plus the height of the rod, ie 12 units, so they would have answered 28 units. They failed to understand the string is taking one of the most classic short cuts in math, the hypotenuse. And therefore the answer is a nice and tidy 5 * 4 = 20.

[@crispyatom]

Easy 20 from pythagorean, wow i feel smart for after soooo many times

[@Jimbaloidatron]

I knew peeling apart all those toilet roll tubes would pay off for me eventually!

[@HPD1171]

@@Jimbaloidatron i still have five hundred and ninety six rolls left and not sure what to do with them other then use them as tools to analyze maths problems.

[@michaelhedrick589]

I did this in like 30 seconds after just flattening the cylinder and doing the exact same thing

[@MaxMathGames]

It's quite an old question, with the geometry solution being the best solution for this question. By the way, great presentation work. 👍👍👍👌👌👌

[@sunchess5950]

Visualisation question for junior classess

[@lucykitsune4619]

Rule of thubm: If you can avoid using calculus, it's usually faster and less prone to mistakes to do so

[@gasp1424]

Im genuinely excited that I got this pretty quickly realising it would the hypotenuse of a triangle of sides 12 and 16 (4x circumference). When you started talking about parametrics I thought I may have gotten it wrong!

[@salbahejim]

I visualized cutting along the string and unrolling it with the flat bottom of the tube representing the bottom of the rectangle and the flat top of the tube representing the top of the rectangle. When uncurled, the cut line would be a diagonal bisection of the rectangle. That rectangle would be the given 12" tall and 16" wide (the circumference of the tube times the number of times the string was wrapped around it). That just leaves a basic calculation of a hypotinuse, A^2 + B^2 = C^2 and you get 20.

[@memelordanimegoddankstar6922]

Solved this in 1 minute inside my head with the same rectangle method shown in the video

[@BaconTheRabbit0]

Same!

[@ArabianShark]

Slightly modified rectangle for me, but ditto.

[@cmuller1441]

Waouh, you are slow... I knew instantaneously what to do and as 12 16 is a 4* scale of 3,4,5 triangle, the answer is 20...

[@jeffreysmith236]

This is the first video I've ever watched of his, and I've watched dozens, where my subconscious instantly knew how to do it.

[@dexter9313]

Somehow I got 16sqrt(2) because I did 12/4 = 4 in my head too quickly... When you trip on the easiest step you feel very ashamed !

[@theimmux3034]

The four triangles popped into my head fairly quickly, felt good to solve because it looked very complicated at first.

[@DownDance]

I did the second one. I was so proud of myself and was completely overwhelmed by the first explaination

[@Roy-K]

The way I thought about it from the start was similar to your trick; there’s four repeating patterns, so find the length of one, then you can easily find the total length. Next consider the pattern: the string makes one full rotation and travels linearly down the rod. A single rotation requires a length of 4, and the string moves linearly a length of 3. Unwrapping the two components, you can see the 3-4-5 Pythagorean triple, so a single pattern has length 5, and the full string has length 4(5) or 20

[@Chriib]

I solved this in my head under one minute using the second method. I truly suck at calculus.

[@Allangulon]

a+b=c in my mind!

[@Loyis]

@@Allangulon sorry bud but that might not really work

[@sprajosh]

I actually thought of unwrapping the cylinder into a rectangle and doing it.. I'm proud of myself 😂

[@jarodmorris611]

I've been designing a DIY drum sander and this is how the sand paper is attached to the drum and how you calculate how long your 3 inch wide sand paper must be in order to cover the entire drum so it was very simple in my head.

[@yac5798]

Well solving that extremely easily by making the cylinder a flat plane and having 4 3,4,5 triangles making the length 20 just made my day

[@XJWill1]

Although the figure makes it clear enough, the word specification of the problem is incomplete. "Symmetric" does not fully describe how the string is wound. The problem needs to say something about the angle of the string being constant with respect to the tube axis, or maybe something about the coils being uniformly distributed along the length of the tube. If the test takers were given the word problem without an adequate diagram, I can certainly understand why they might have had difficulty.

[@PolishGator]

Thank you. Based on the wording, the answer can easily be 16. The length of the cylinder is irrelevant if the string does not wrap from one end to the other(the missing piece of info).

[@XJWill1]

@@PolishGator I'm not sure what you mean, but that is not "the missing piece of info". Symmetrical refers to symmetry, not an even distribution of loops or a constant angle of the string with respect to the axis of the tube. THAT is the missing information. Otherwise there are infinite possibilties. For example, it could loop 1.5 times at one end very close to each other, then go on a long loop to the other end and then 1.5 times at the other end very close to each other. That would be symmetrical and extend to the ends, but it would not result in a length of 20.

[@PolishGator]

@@XJWill1 So if X is the diameter of the string and the length of the rod is equal to X, the string is basically wound in a perfect circle around a VERY short rod...It would also constitute symmetry. We are saying the same thing, just picturing different possible examples in our imagination. The problem needs more specific details.

[@Its__Good]

Me: When is your next video out Presh? Presh: How longs a piece of string? Me: Was only asking . . . . .

[@cigmorfil4101]

Actually...how long _is_ a piece of string? You just need to work out the diameter range that would be considered string as opposed to, say, thread or rope, the minimum length that is reasonable to call a piece of string and the maximum length would be dependent on handling ability - there would be an upper limit based on the size and weight of drum full of string (the length of which would be dependent on the diameter and density of the string). Once you've worked all that out you can give a fairly confident range to how long a piece of string is...

[@SgtSeth]

I am a radio/RF technician and I saw this problem as wavelengths. Knowing that the overall length was 12 and 4 was the circumference, I guessed 5 as being the wavelength from trough to trough. I guessed 20, so imagine my surprise when I was correct!

[@SirCatsal0t]

I solved it by looking at one 4th of the string. The rod is 12 long so i divided it by 4 giving me 3, I knew the circumference was 4. I then mapped out the coordinate x3y4 on a piece of paper and drew a line from x0y0 to the point. The length of the line was then 5, so i multiplied it by 4 again giving me 20. It went a little different in my head but it feels pretty nice being able to solve stuff like this.

[@Gnastygnorc]

I solved it using calculus. Even though there was a simpler way, its nice having such a flexible tool.

[@meocats]

Congratz you failed the question then, because these are timed. To find the answer you must know the answer!

[@Gnastygnorc]

@@meocats Ich have no idea what you are talking about.

[@plus790]

Paused the video at :34 and came up with an answer of 20 within 10 seconds by slitting the tube and laying it flat.

[@guycxz]

I did a similar thing on one side of the cylinder. Since the string is symmetrical you can essentially treat each one of the 4 wrappings as an isosceles triangle, then draw a height from it to the bottom of the cylinder. You unfold the string alone and get 8 triangles that are similar to the 4 in the video (2 to 1 ratio). It's important to remember, however, that 3/2 isn't 4, otherwise you'll get 8sqrt(8) instead of the correct result.

[@rays3761]

Figured out the simple trick in a couple minutes. Good stuff!

[@GiantKush]

I did something similar to the second solution. See the string view around the rod 4 times. And the length of the rod is 12 cm. This means at the strings will be 3cm away from each other. Now for easy visualisation, cut the rod into 4 equal pieces. And then flatten each piece. The string will be equal to the diagonal of the rectangle formed and the dimensions of the rectangle would be circumference x distance between two points on the strings i.e. 4x3. Hence the length of the diagonal from Pythagoras (Gougu) Theorem will be 5. Since there are 4 such pieces, the total length of the string will be 20cms. Anyone who did something similar?

[@sunchess5950]

Just simple imagination required no calculus it will make it lengthy

[@UnimatrixOne]

Gougu = thumbs down!

[@johncourtright1632]

Same. Very satisfying.

[@jonniejlo]

Nice! I imagined the cylinder was like a paint roller. It rolled 4 revolutions creating one big rectangle (12x16). The string length is then just the one diagonal. One equation! Boom! I love these videos. Thank you Presh 👍

[@jeanpauldelauw7716]

Simple Pythagoras, no calculus needed. Solve it in under 1 minute ... square root of 12²x16² =20

[@peteiiseasy3217]

oh yeah

[@ludomine7746]

Figuring it out when pausing the video and being correct is absolute bliss

[@ghostbluster8900]

In my head, the string was at the same time circling the cylinder AND going forward. I added those two element together as i would to take the norm (ratio?) Of the vector. I also sliced the cylinder in 4 parts to ease the calculus. I did not unravel the cylinder though

[@92ivca]

As an engineer this was easy. We usually calculate the length of a thread in a bolt, using the pitch distance and the diameter, at the same way you did in the second solution.

[@GordieGii]

And you would probably have used the pitch diameter, rather than willfully ignoring the thickness of the string.

[@chhabisarkar9057]

The last technique was neat ! ;)

[@mr.eaglerider7217]

Chabbi sarkar from unacdemy

[@ZelenoJabko]

I needed 30 seconds to figure it out.

[@kids_learning_channel4810]

@@ZelenoJabko nice

[@lakshaygupta9061]

Ikr!

[@curiosity5697]

I did this in my head and I'm proud of myself! It's the first one on this channel I actually managed to do.

[@bb2fiddler]

Beautiful problem! Thanks for uploading

[@GioFaber]

The beauty of math!

[@amarug]

I saw the pythagorean relationship in about 30 seconds, so the problem was solved in my head in about 35 seconds. Engineer by training, used to always "unwrap" problems 😅

[@admiraloscar3320]

My guess before watching the solution: Circumference=a Length of rod=b Length of string=c (a*4)^2+b^2=c^2 (4*4)^2+12^2=c^2 16^2+12^2=c^2 256+144=c^2 400=c^2 sqrt(400)=sqrt(c^2) 20=c So the length of the string is 20

[@frentz7]

GREAT video. .. Note that the transformation from cylinder to rectangle preserves lengths, ie there is no distortion.

[@paulmarquardt6881]

I solved it in my head and then watched the first solution like 'wait it's so hard I'm probably wrong' but when I had the right solution and you explained the easier way (which I used) I was happy that I was right

[@Scaw]

Same here.

[@tahafen5408]

me too, it's hard to believe that only 10% of students answered this question, it's not that difficult.

[@CarolynDesign]

@@tahafen5408 It's not that hard when you approach it looking for a simpler alternative. But, when in the middle of a high level math exam, where most problems have required using the calculus method, it's easier to miss the "easy" method. That's one of the great tjings about "Mind Your Decisions", is that Presh shows both methods, and encourages out of the box thinking as an approach to problem solving.

[@Allangulon]

Doubting yourself is a sign of intellect! Just don't doubt yourself too much.

[@Allangulon]

@@CarolynDesign Most require method to be explained so the calculus must be displayed!

[@jamesmnolan]

Like most of the other braggers here, I too got it quickly by imagining unrolling the tube and it was super easy and quick. What is surprising to me about all those people who had trouble visualising this shortcut, is that it's staring you in the face in everyday life - the cardboard inner tube of every toilet roll and kitchen roll is constructed this way. Just take a look at one in your toilet or kitchen (once the paper has all been used) and the helical seam is equivalent to the string wrapping round... no genius insight required, just the ability to pay some attention to everyday objects around you. Maybe I'm a weirdo but I always look at these things and wonder how they're made!

[@eduardokerber2931]

the pressure of an exame does things

[@urekah37]

Thanks for making this video I was thinking about a similar problem this helped tremendously. Thanks again.

[@sagittarius5466]

Surprised people struggled with such an easy puzzle

[@DojoMaster21]

Solved in 3 nanoseconds

[@Michael_Mears]

Pythagoras theorem FTW!

[@UnimatrixOne]

Gougu = thumbs down!

[@WhiteAce3]

My mouth fell open when I saw the flatening trick. Thanks. This will help me a lot in future

[@reetjaiswal3950]

Since my experience with helices is only from magnetism, I tried applying that by assuming the string to be a helical path followed by a particle in a uniform magnetic field, it was pretty easy from there. But i guess the triangle method is cool too

[@user-hj3js2dl3r]

Lol seriously? I just tried randomly and logically using theorem pythagoras to solve this? I think this is my 3rd time to solve mathematics' problems from mindyourdecisions channel? Thanks God my logic still works :')

[@lyde4899]

I literally found this under a minute. It might be luck but idk it seemed so obvious

[@peteiiseasy3217]

@@lyde4899 true

[@paulrinaldi2209]

I’m 13, and I got it with Pythagorean theorem 😂 Edit: I solved it like the cylinder was just a flat space with a line going diagonally from one corner to another

[@peteiiseasy3217]

cool

[@meocats]

Of course you did because you don't know calculus, pytagoras is all you had and you tried your luck. This is a question for adults, who understand why unwrapping a cylinder produces lines. That's how only 10% passed the question. They took too long to see that. Most tried to derive and waste time - you get very little time per question. Probably no one guess because if you guess you're 13 and kids don't take this exam.

[@uwelegalo3412]

this is a very nice visualisation for transformation from carthesian koordinates to cylindrical coordinates. So in theory the second aproach is actually also done using calculus but with a very smart way to get rid of weird formulas. I like that. Good Video.

[@SteenWinther]

There is really nothing difficult about this problem when you are an engineer. It is equavelent to a thread with 4 revolutions which can be envisioned as a triangle wrapped around a cylinder. The base of the triangle is 16 (4 revolutions of circumference 4), the height is 12 (height of the cylinder, Phytagoras gives us the length of the thread as the length of the string: Sqr(12^2+16^2)=Sqr(400)=20. No fancy 'tricks' needed!

[@fbi6893]

good thing i know about the 3-4-5 triangle, now i dont have to use the gougu theorem

[@rekhasily]

I just solved it without your explanation and my solution was type of your second explanition

[@tyalks.5763]

the method I used was a bit different but only took about 20 secs. I defined two vectors, the x-vector = 4x4=16 and the y-vector = 12. since their direction is 90° apart I used the phytagoran theorum = root of (16^2 +12^2) = 20. I learnd this trick while calculating flight paths.

[@dammitdad]

Love it. Took a few minutes to work out. Well laid out problem with easy numbers.

[@procodezandcoderzPingle]

Me sitting here with 16 👁️👄👁️

[@matichocevar4004]

I calculated 20 in like 20seconds with 2nd method.

[@abchitte]

Me too

[@viniciusfernandes2303]

Thanks for the video!!

[@SaturnusDK]

There's actually a formula for this problem which is occasionally used in electrical engineering; l=(L^2+(NC)^2)^0.5, where l is string (coil) length, L is rod length, N is number of turns, and C is circumference.

[@menovat]

I figured out the trick. Enjoyed solving this.

[@jacobc2850]

16 is my guess let’s see how it goes! Since I’m thinking it’s just wrapping it around a circle 4x Edit: Darn it’s 20! Still very cool and I like the second explanation!

[@techmad8204]

mrx2135 ravenger yup it contains a bit more of string

[@christophersmith8014]

Since it's basically just a rolled up right triangle where the string is the hypotenuse, the number of turns has a direct relationship to the circumference. If you half the number of turns and double the circumference then you also get the same result. So, if you reduce the number of turns to one (which requires dividing by four) and multiply the circumference by four (which yields sixteen), then you can take the length of the rod as the base of the triangle and use the circumference of the rod as the length of the other leg. You can then solve for the length of the string as the length of a single hypotenuse, which in this case is a 12,16,20 (3,4,5 triangle ratio).

[@truckjumperdude]

i did it by using the pythagoreum theorum by using 3 and 4 as the lengths of the leg and i got 5 for one segment and then multiplied that by 4 to get 20

[@ashrafhassan6610]

Well I'm from those 10%💪😀 But I've done it with the simple way .... never thought of a calculus solution!

[@blackpinktanked6809]

the last trick was soo ☝️☝️☝️🔥🔥🔥

[@dennisjones8581]

I had no idea how do to it using calculus. I just flattened it out in my head and had it solved before the explanation was done!

[@gregneidlinger8252]

I did something similar, but with one big triangle. If you imagine "unwrapping" the cylinder, the base would be 4*circumference because the string wraps around 4 times, then height is as listed and the boul Pythagoras does the rest of the work for you. I used the same trick to help my dad determine how much material he'd need for the banister of a spiral staircase for some contracting work he was doing.

[@shmuelpollak3272]

***THUMBS DOWN FOR GOUGU***

[@fdhyunseo]

I am 13 yrs old and I solved it in 40 seconds Yay It was one of the most enjoyable question! gg

[@aldoushuxley5953]

I think it is one of those problems, where younger people think it is easier. If all of the problems before required calculus, maybe people might be tricked to think they have to solve this that way too, and overlook the forest for the trees. (There are a lot of inteligence tests in which primary schoolers perform better than adults. The most famous one is taking the numbers 12345, cutting the upper part of, and mirroring it. What is the next number? Most adults fail this :) ) I thought it was relatively easy too. Don't know why so many people failed... Congratulations to your solution

[@samaryadav7212]

I am 14 years from India and I too solved this problem within 1 minute.

[@MohammedNameerAnsari]

@@aldoushuxley5953 so what's the next number?

[@aldoushuxley5953]

@@MohammedNameerAnsari Maybe I did not describe it well. My english is unfortunately still pretty bad... I mean the sequence of the natural numbers. (so 6) But you don't show them 1 2 3 ... Rather, you cut the numbers horizontally, and mirror them along that axis. So 1 becomes I... Sorry, I can't describe it better than that. Doesn't matter though. The point is, that some puzzles are easier for young children, because they look at them more openly. A trained mathematician or physicist might look at the problem, and think "oh, I can solve that through integrals" without ever considering, that there could be an easier solution, because he was trained to solve problems like this that way. A child doesn't know about integrals, and has to analyze the problem with an open mind.

[@MohammedNameerAnsari]

@@aldoushuxley5953 ok bro👍🏻

[@bencoder]

Unroll the rod: 4x12. Split into 4 sections of 4x3. Diagonal of one section: sqrt(4^2+3^2) = 5. Times by 4 = 20

[@cashkurtz5780]

I figured it out before the answer was given, and it was in the way of the "simple trick". Turns out knowledge of euclidean and spherical geometries is really helpful in this situation.

[@lycheejuicelichigaming2263]

This was easiest problem lol 😆 (in my opinion), solved under a minute in the head.

[@electricwizard5747]

no you didnt

[@shrawon3605]

I am one of those 10% who say they belong to the remaining 90%

[@sunchess5950]

Oo lol

[@holyknight51]

Solving before watching, the string is fixed in radius using a cyclindrical coordinate system, but moves in angular and z hat directions. find the magnitude of these components, and use pythagoras to find the total magnitude. in other words, the length = sqrt(Radius*anglerotatedindegrees^2 + length^2)

[@michaelweiske702]

I believe I had a similar problem irl with a tube we wanted to wrap glow-sticks around. The way I solved it was by first asking how many times we wanted it wound, in this case 4, and how long it was, in this case 12, and what the circumference was, in this case 4. First, we divide the rod by the amount of windings, so 12/4 is 3, and we say it is h. Then we already have the circumference which is 4. If we unwound this rod like a scroll or map so that it was flat, we would see that the path the string takes is straight, and thus we can use the pythagorean theorem to solve, with the base being 4. 3^2 plus 4^2 is 5^2, so the length is 5. Then we multiply it by the number of wounds, so the answer should be 20. Edit: It appears my solution more or less matches the simple trick of this video. The calculus solution was also interesting, but I feel it is less elegant. The best solution to a problem is usually the easiest one, after all.