Can you solve the banana puzzle? 

I used pounds for the mass unit and pounds for the currency. That way units cancel out and nothing has meaning anymore

Honestly the Banana for Scale reference being 15 years old was the wildest thing I've heard in a few days

Matt sees a banana hat. He thinks to himself "how can I make that a business expense?".

Love the “SnatchBlock” interruptions from SmarterEveryDay

I was thinking: "The scale says 1.6 so they'll cost 1.60£." without even considering the mechanism as a part of the puzzle. To me the puzzle was "The bananas weigh 1.6 kilos and cost 1£ per kilo. How much do they cost?"

So the answer is “the shop scale isn’t calibrated correctly”.

Plot twist: The scale is calibrated taking into account the pulley system below. Bananas weigh 1,6kg

"I can't remember the name of james grime's channel right now ;)" had me rollin. For those who don't know, it's "SingingBanana".

I too exist primarily on out-of-date references

My first thoughts were: since the scale is used in a store in this specific way in order to weigh fruits, the scale would be calibrated to show the correct value. I should have known better, seeing this is a maths channel after all.

as a wise professor once said: draw the free body diagram

3:53 This moment is when I found out that the horizontal line at the bottom of the image was meant to represent the ground and not a stick-shaped counterweight.

Did not expect Destin in this episode.

I solved it like that, without actually doing any maths: Lets say we replace the attachment on the right with another identical set of bananas. The pulley will then act as a balanced scale and stay in place. We are now weighing two sets of bananas, but from the point of view of the pulley nothing has changed, the rope sees the pull of bananas from the left and the same pull from the right. Therefore, in both situations the scale will show double the weight.

You know you should probably make mention that it's a pulley anchored to the ground before giving people time to solve the puzzle. It's not entirely obvious what's going on until that's made clear.

Ah yes, the banana will be "berry upset." How pleased were you with yourself when you came up with that one, Matt?

So the answer is "call whoever is responsible for regulating scales used in trade"?

So the real question is then "why is the scale not calibrated properly?" I feel like I'm back in school with bad textbook tasks that assume you hate what you're doing and have the quality to reinforce that sentiment.

Why did the banana go to the doctor? - It wasn't peeling well!

The bananas would still cost $1.60 so the store could make more money.

*"How do the bananas feel"* - Matt Parker 2020

I mean I just assumed it was some kind of weird scale and that it was calibrated to accurately show the forces involved, not that it was some kind of "Aha! gotcha!".

The simplest way to approach this: Detach the string from the ground, To the detached string, insert a weight, which would cancel up the rotation of the setup, You are ending up with two banana weights pulling down on the weight. Therefore, the scale would show up double the amount, so the bananas weight half of the value showed by the scale. I don't think it could get any simpler than that.

going into a grocery store i have to asume that their scale setup displays the right amount of mass, so the scale would be calibrated to show the right answer, regardless of the pulley setup

Great fun. Classic statics problem. The one issue is that if this were an engineered device in an actual store designed to measure the weight of fruit, the physical marks on the scale would be *calibrated* for the system that it set up to measure.

but in a supermarket scenario, why wouldn't the scale be recalibrated for the double force in the same way that it's been clearly calibrated for the acceleration due to gravity??

Banana who feels forgot about singing banana.... *Sad banana noises*

“Nothing here can curve at all, which, for me, feels very unnatural.” It’s all worth it for this single pun

Another simple way to answer the puzzle, without building the system, is to change the system a little bit, to something equivalent. Just hang the same amount of bananas on the right side, instead of hooking the string to the ground. Why the same amount? to keep the bananas on the left side hanging with no movement like in the original system. This way, the scale keep showing 1.6Kg, and now it's pretty obvious, the bananas on the left side weighs half of it.

My answer was "if the scale was designed to be used in that way, with a pulley, then obviously it's gonna be recalibrated to show the real weight and compensate for what the pulley is doing, so if it says 1.6kg then it's surely 1.6kg."

Love that Arrested Development reference! I'm sure dozens of us caught it!

Such chaotic Destin energy happening throughout this 😂

While the problem solving here is technically correct, the problem is that it completely missed the obvious. In a common setting such as supermarket as presented, you would halve any value on the display to account for the ""double pulling"" effect, since you would not expect customers to know of this and to half it in their head. From a purely mathematical standpoint, its 0.8, but for a common, every-day scenario like presented, its 1.6

The setup doesn't matter; what matters is that the store should be setting up their scale and bananas in a way that what you see is accurate. If their scale's scale is not tuned, it's their fault if the reading is incorrect.

While dressed as a banana he can't remember James Grimes' RU-vid channel. Maybe if you sang it you might remember.

The practical demonstration made it MUCH clearer.

The banana getting annoyed at the work equation is comedy genius

Me thinking: "Yes, yes, i understand it's a math problem, but are you telling me the store didn't zero their scale? I'm never shopping there again!"

2:42 Thank you Mr Parker for giving me a greater appreciation for all the small but cool/fun things maths teachers do

As soon as i saw the pulleys i thought of Destin from SmarterEverdyDay, great job

My first instinct was that the scale would be calibrated to take any mechanical advantage into account. If it said 1.6kg...that it would actually be 1.6...because the scale would be designed to this purpose.

The watch-face part of the pulley is just poorly calibrated

By the way, the most general version of the work = force×distance formula is that work is the line integral through the force vector field over some curve that the object is moving along. If the path is always in the same direction as the force, the line integral simplifies to a regular integral. And if the force is also constant along the path, the formula further simplifies to the given W = Force×Distance.

It depends on if the pully is accounted for in the calibration of the scale. All kinds of scales have built in mechanical advantage between the load and the strain gauge. Also depends on how crooked the shopkeeper is.

Domesticated engineer implies wild and free engineers

Intros are getting better and better.

Those destin references are brilliant

Your videos are always funny and great, but this one was funnier than usual! Thanks for a good laugh!

Can I note that a good part of this is a nice little physics/engineering problem. Knowledge of the tension forces and the "dynamics" of the banana scale like this are a good little intro to pullys and how they work. :) Really neat to see it getting around the internet.

To keep things simple, I just imagined replacing the other side with identical bunch of bananas. As far as the lower pulley is concerned this is indistinguishable from the force on both sides perspective. If 2 bunch of bananas weigh 1.6kg, each bunch should weigh 0.8kg.

The time's up thing really got me. 😂

Matt: I'm gonna show you how to use a banana to tell when your time's up. Also Matt: *Wear's a banana* Hey! Time's up! Me: *I just cracked up*

this mostly tells me that the scale is improperly calibrated for its installation

*Everyone asks how the bananas peel no one ever asks how do they feel.* LMAO I cried!!!!

Haven't watched to the end. I'd say that the scale reads twice the bananas' mass since we could replace the anchor with an identical set of bananas and the setup would remain the same.

I found your closing pun very ap-peel-ing. So glad you managed to slip that one in.

As an engineering student, I got stuck at the part where spring scales don't measure mass.

but Matt! if it's setup in a supermarket, it would need be calibrated to match trade regulations. there would need to be 1.6kg of bananas for it to read 1.6kg. otherwise it's illegal bananas. -watson

I love the Destin cuts lol

I need more Banana that Feels.

I didn’t even realize until you started explaining it that the bananas were being weighed over a pulley with the other end fixed. It would have been helpful for that to be explained beforehand. I didn’t realize what the puzzle even was at first.

Matt: Does a show with bananas Also Matt: Can't remember Grimes' RU-vid channel name LOL!

The indoor boomerang is really neat.

Such a fun puzzle!!

Everyone asks how the bananas peel, but no one ever asks how do the bananas feel. I felt that

seems to me that if the store scale says the bananas weight 1.6kg, they're gonna charge you for 1.6kg of bananas!

Practical example of sacrificing force and winning speed - hydraulic elevators. Where you have a hydraulic piston pushing on the pulley from below, which then "shoots" the cabin up at twice the speed. Can be seen in action at the London's Docklands Light Rail (DLR) stations. PS.: 30g weight will go up (unbalanced forces and stuff).

to simplify: imagine if it were a weight on the other side, rather than an attachment to the ground. if the weight is the same mass as the banannas then it will be double, and the weight and banannas will be in equilibrium. now, why do they sit in equilibrium? well, because the weight of the banannas on the string are being counteracted by the weight of the weight. if that weight were not on the string itself then the banannas would fall off. now, what is different if we replace that weight with one heavy enough to rest on the ground, or the ground itself? now the banannas are still pulling the same amount, and they are still being counteracted on the string, so the string must be lifting that much weight, and thus still putting double the weight onto the scale.

I'm just going to make a comment about 'one pound per kilo' as they are both units of weight when said aloud and go away again..

It would be so much easier to just replace the ground tether with another equally heavy set of bananas, both being equivalent in terms of tension.

Having only looked at it up to 1:09 my answer would be as follows: The scale shows 1.6kg, which suggest a price of 1.6. But we have to account for the counter weight, which means that the banana + counterweight together are 1.6kg which means the banana only weighs 0.8kg which leads us to a price of 0.8. BUT we also don't know whether the scale is nulled to account for the pulley system, which means that the banana + counterweight + pulley system together weight 1.6 kg, which would mean that the banana should weigh even less than the 0.8kg which means that we should have a price under 0.8, which is not one of the options given. In short, if the balance is nulled toward the pulley system then it's 0.8 for the banana, if it's not then it is unkown and undeterminable how much the banana actually weights and thus actually cost (as, if we ignore physics and look purely at the math, the pulley system could weight anything between 0 and 1.6kg and thus make the banana weight anything between 0 and 0.8kg). Edit: Ok, so I apparently missed that there was no "counterweight", but that it was statically attached to the ground. Which doesn't change anything and I still maintain my answer that it's unknown because we don't know whether or not the scale accounts for the weight of the pulley or not.

Thank you so much for uploading this video. It is helping me to get through the pandemic!

Took me until Hugh's demonstration to understand that the metal platform on the right was supposed to be fixed to the ground. I thought it was balanced by the weight of the bananas the whole time, which didn't make any sense if it was weightless.

This video is a-peeling. ... I'll see myself out.

Your election analysis videos may have been the first of your videos I watched, but I subscribed after seeing all the silliness in your older videos :P

Went to a maths inspiration in 2015 and it was honestly such a great show, now currently completing my masters in mathematics

Nope.

1.6: The scale says 1.6 kg, so it must be 1.6 pounds. Surely the store will have this calibrated proper in order to not confuse customers, right? .8: Well, ackshually...

I don't want to admit how hard I laughed at the "time's up" bit...

Always appreciate an Arrested Development reference.

oh. so that's grounding on the right? i though this is just some kind of funny or not drawn properly weight which counterweighs bananas. and so i thought overall weight is 1.6 kilos and they're in balance therefore bananas have to weigh half of pulling weight

MPMP false alarm :>

Hey matt, I love using mathematics for practiical inspiration, and loved your lecture way back when about probability and human's tendencies to misestimate it. It steadily started from mathematical concepts and applied very quickly to a life lesson. I speak a lot about these sorts of things, but your presentation skills and crowd apathy really makes your speakings what they are. That said, would you be interested in making a video to explain things like the heisenberg uncertainty principle, chaos theory, and qunatum mechanics in a scope as to relate them to taking advantage of each moment given and that what happened in the past doesn't doom you for your future? And in the event that you've already touched upon this, could I be directed to that? I've found people are inspired most by what they can prove to themselves, and that being particularly fundamental to maths makes it a perfect tool. By the by, really cool idea for having an event "conducted" by the kids, no doubt more engaging and meaningful.

I found it useful to think of the pulley as a lever with the load in the middle, hence 2x force multiplication.

Well, assuming this contraption is used in a grocery shop it must comply with the Weights and Measures Act and be calibrated correctly. Therefore I have to assume the weight displayed (1.6kg) is correct, meaning the bananas cost £1.60. That's real world practical maths. So there.

Can we assume that the pulley's weight is compensated for? Because the standard scale would not...

I'm berry impressed in the casual use of that pun with bananas.

"I forget the name..." I laughed much more that I ought have.

Stand-up Maths : "can you solve..." Everyone : *Ted-Ed flashbacks*

I'm a simple man. I see Matt Parker, I click. Also, did you ever end up finding a solution to the Parker Square?

Here is alternative way to explain the result: Imagine instead of the string being anchored to the ground it is connected to a counterweight of equal mass to the bananas. Now it is pretty obvious that the total mass pulling down = mass of bananas + counterweight of equal weight = 2 x mass of the bananas. Next you only have to realize that in the equilibrium there is no difference (In forces, tension etc.) between anchoring to the ground or using a counterweight of equal mass. The same thought experiment can be applied to the more complicated setup by replacing the middle anchor with 2 bananas and the right anchor with 1 banana in a nice symmetrical fashion, everything is balanced out and the total force is equal that of 4 bananas.

For some reason I thought that the bananas were counter-balanced by a sheet, so they're obviously half as much. Maybe if there were a couple of lines beneath the horizontal line, I would have realised it was a ground...

Wait, that's not a maths puzzle.

If they display it that way in the store, the must have calibrated the scale to show the correct mass, so it should still cost £1.60. Otherwise i would be a misleading scam.

*_Suddenly Destin_*

That little Destin clip around 2:55 made me giggle, I immediately thought of that video when I saw the banana set up

Actually the banana puzzle was missing one important information: How is the scale callibrated? If I see an apparatus like this, I have to assume that the scale is properly callibrated so that it shows the correct weight within that apparatus. If the callibration is something that I can rely on, then the scale could show basically anything. In this case the scale is not properly callibrated, it is callibrated for a different usage. This makes the whole puzzle a little bit meaningless.

What do you mean answering £1,60 means "they couldn't figure it out"? I mean, if that is how they measure weights in that store, then surely their prices are for the weights given by the measuring system.

The way I would word it is that the banana + pulley + rope system is experiencing three forces 1) gravity of the banana downward, 2) the downward tension at the fixture by the ground on the rope, which is exactly equal to gravity on the banana, and 3) upwards tension on the whole thing, which is what the scale sees. 1) and 2) are balanced by 3), so the upwards tension = downward tension + banana gravity = 2 x banana gravity, so the scale reads double the banana's weight.

I like these interjections of clips from Destin's video on pulleys. We need to make this a meme(if it's not already). Much like the FULL BRIDGE RECTIFIER thing.