Rob asks a simple question, and you can see the problem before your own eyes, but how easy is it to work out the answer? Oddly, a pack of cards helps here.
However when someone asks, ‘Which is heavier, a pound of feathers or a pound of gold?’ do not say they’re the same because they’re not! Feathers are measured in avoirdupois weight at 16 ounces to the pound - gold is measured in troy weight at 12 ounces to the pound 🧐
I love that the information is often presented as a couple of buddies trying to outwit each other. I really think it makes the concepts appeal more to younger people especially young boys.
Competition is also great for progress and learning. Watching 2 people play catch? Neat. Monkey in middle? Now ya get to see how people get out of the middle
I bet very few girls watched this show. You can see this on TH-cam as well. Videos on math and science clearly get almost exclusively comments by men or boys. Women seem to be much more interested in other stuff, like ... well I don't know. (Pets? Makeup?)
For those who want to math it out: If each cup has 90ml, and you transfer 10ml from the coffee cup to the water cup, then the water cup will have a 100ml mixture of 10/90 coffee/water ratio. Meaning that 10ml of this mixture would consist of 1ml coffee and 9ml water. Removing that 10ml from the water cup would leave only 81ml water and 9ml coffee. If you then transfer that 10ml back to the now 80ml of coffee, then the coffee cup will have 90ml again, but will only 81ml of it will be coffee and 9ml of water. There is exactly as much water in the coffee cup as there is coffee in the water cup. That’s all this experiment was trying to demonstrate.
Well, the thing is that you have explained the case where the mixture is perfect. It is a special case. What was shown with the deck of cards was that it works in the general case where the mixture is not perfect as well.
@@Sauromannen In the case of the cards and the liquids, it is the same because: 1. The quantity of each type of liquid/card is conserved 2. The same amount of liquid/cards is in each glass/hand. The same quantity of each liquid has been moved from each glass to the other because the same quantity of the other liquid must be moved the other way to replace it to keep the water level. If you always have 10 cards in each hand, and there are 10 cards of each type (face up and down), then if there are 2 face up cards in your deck (thus 8 face down cards), then there must be 8 face up cards in the other deck (thus 2 face down).
@@styraco4739 you did not understand my point. The mixture of the liquid does not have to be as shadowstalker or Katherine showed. They are not wrong but show only the special case where the mixture is perfect. It does not have to be perfect as can be illustrated by the card example.
@@styraco4739 In reality there's no way to know if you grabbed the same amount, unless the substance is perfectly homogenized and you are indeed capable of grabbing the exact same amount and there was no loss of liquid in the transfer. There always is and it doesn't matter for real world purposes but if you're showing scientific exactness it does need to be accounted for in the equation. The card example works but the liquids do not. There's roughly the same amount but that's really the best you can say.
What made it click for me was thinking about the maximum and minimum limits with the card example. Remember, the question was about the final ratio of water to coffee being equal in each cup (or deck), regardless of the amount. After the initial three cards went into the "water deck" and it was shuffled, he said you can choose any three cards to put back in the "coffee deck." So what if we chose 3 "coffee cards"? OK. The ratio would be back to the starting amount, yes, BUT it is equal, as the same amount (zero) has been transferred. If you chose 3 water cards to put back then there would be three water cards in the coffee deck and those three original coffee cards left in the water deck. Equal.
There is a semantic argument, with the phrasing "have I added more of coffee to the water cup or more of water to the coffee cup" is imprecise. But the real answer is so much cooler!
@@CycleMantis The biggest semantic issue here is that there is already more water in the coffee than actual coffee. So one could say that you swapped equal amounts of each glass, but not necessarily equal amounts of coffee and water. The play might work better with something like coffee and milk.
@@patrickkeller2193 no, that's incorrect, it's beside the point what solutions you have in each glass to start with, after the final transfer you'll have the same ratio in each glass. even if the coffee solution is in fact 75% water, the end result will be the same ratio of water/coffee in both glasses. as long as the fluids you are using are soluble and mixed evenly this equation will work with any substance.
It was actually pretty dumb, because you won't always randomly pick the same cards, so there is probability involved, where in the liquid there is not.
@@blindi6326 The liquids are made of molecules which move around in the glasses more or less randomly. Probably more randomly than card shuffling. So it's actually a perfect analogy. Maybe go back to school before calling people dumb?
@@blindi6326 the point is, you don't have to randomly pick specific cards. It works with any amount of cards, and any sized bunch of cards. The only requirement is that the amount you switch is the same both ways. So you could do it with 21 card deck, take 8 from one side over to the other, then take 8 back. Doesn't matter which 8 you choose for the return, it will always end up with equal amounts switched. So 8 coffee over and 8 coffee-0 water back, 7-1 back, 6-2 back, 5-3 back, no matter which 8 cards you send back there will ALWAYS be equal representation. That's the point.
@@blindi6326 but with his example in the video, if you brought all 3 coffee cards back then there's be zero opposite cards on each side. If you bring two coffee card back there'd be one opposite card on each side. If you bring one coffee card back, there'd be two opposite cards on each side. If you bring zero coffee cards back there'd be three opposite cards on each side. No matter what you do, the mixes stay exactly opposite with the same amount of the other card left.
Magician here: For anyone interested in learning the actual card trick this relates to the routine is commonly known as the "Oil and Water" card trick and there's probably dozens of demonstrations on how to learn and perform the trick. It's a classic of card magic and a fun, interesting and self working routine that will have your spectators completely astounded. Enjoy.
@@AksTube it's a play on words for the game which my channel is about. The game is called Rally Fury and when you get frustrated playing it you get Really FURIOUS.
The cards are a very helpful way to understand the bottom line of this problem. If there was more coffee in the water glass than water in the coffee glass and both glasses had equal volumes, we would be asking what happened to the missing water!
crapstirrer I sympathise. Take ten red cards and ten black cards, mix them up and separate into two piles of ten. If one has 7 to 3 then the other must have 3 to 7. I guess you don't have a problem with that. Maybe your problem is how this is analogous to the dilution of coffee? Me too. It isn't. Starting from a glass of salt water and a glass of pure water we know that salt water is denser, it contains more matter per unit volume. So the first transfer by volume carries more matter than the second.. The transfer is equal by volume but not by mass. The answer given is right if the judgement is by volume but wrong if it's by mass. So the question asked is vague. Don't get me wrong, as a 63 year old child physicist I adore this channel !
not exactly. according to the law of conservation of mass as long as the same amount of matter is in both cups, the ratio will be the same between them. You can't have more coffee in one cup when the same amount of water needs to be in the other cup to keep the balance.
Because you have taken away a spoonful of coffee to begin with there is less coffee in the cup before you return the water/coffee solution to the coffee cup.
Yes. There will be less coffee in the coffee and less water in the water than there was in the beginning. But- the same amount of water will be in the coffee as coffee in the water.
Look at it this way : The first spoonful is 100% coffee , the second spoonful is now less than 100% water but is now added back to a lesser volume of coffee . So the coffee/water ratios remain exact opposites from one glass to the other until they are both 50/50 .
That's a great ad infinitum explanation. If you transfer back and forth an infinite number of times, they'll both be equal. Therefore the ratios getting discussed must have always been equal.
But the second spoonful from the water isnt all water. This doesnt make any sense. The cards are a bad example as they arent a homogenous solution they are separate entities. The water and coffee become the same solution
@@yeelahowah7476 I thought it through last night. The way I finally understood was more coffee in more water=Less water in less coffee. Idk if that makes sense to you
The question itself is what’s confusing. The conclusion is just saying that both cups have 95% of one thing and 5% of the other. Well, duh. That said, “pure coffee” is itself mostly water 🤔
What an amazing puzzle! Or is it a conundrum? I guess both? Anyway, firstly, the question is a bit poorly worded. What they asked is "have I added more of this (coffee & water mixture) into this, or this (water and coffee mixture) into that? Well, you added more coffee into the water cup, but you also took out some coffee of that cup later. However, the question is intended to be "is there more water in the coffee cup, or more coffee in the water cup - or are these quantities the same?" To this, the answer is that they are the same, _regardless of whether you mix properly after the scoop._ You could do this with cards, shuffle them randomly, and it always works. This is because the remaining coffee in the water cup will be 1 - (the amount of coffee you transfer back with the second scoop), where "1" is the full original scoop, and the water in the coffee scoop is 1 - (the amount of coffee you transfer back with the second scoop), where 1 is the full second scoop, but the second term is however much of that scoop is occupied by the coffee you had just put in there. You can see that these two terms are the exact same! The paradoxical or counter-intuitive feel of the puzzle comes from the fact that we mostly think "we just put a full cup of coffee in the water cup, and we only put slightly less water back in the coffee cup". However, this fails to account for the fact that when you take the coffee to the water, it's 100% coffee, while if you take some water to the coffee, you just fill the remaining part up with coffee you had just transferred. Less water means more coffee at the exact same rate, as shown above! So you put more coffee into the water cup, but you never took any water back to the water cup. You did, however, put coffee back into the coffee cup - exactly the difference between how much coffee you put into the water, and water into the coffee. So hopefully, that not only provides a solution / "proof" to the problem, but also one that is intuitive, along with an explanation of exactly where most people go wrong in their thinking and why. I originally got this wrong because of the flawed reasoning I described above, and I find it incredibly interesting to find out how my mind can be so easily tricked. Hope y'all do too.
"Will the ratio of water to coffee in this glass be the same as the ratio of coffee to water in this glass?" That was the question. That was the point.
Cards and water are different. If you put coffee in the water now the water is no longer 100% water. perhaps it's 90% water and 10% coffee. Now you take a scoop of what is only 90% water and 10% coffee and you pour it back into the coffee. You have poured 10/10 of coffee into water but you have only returned 9/10 of water into the coffee. Therefore you put more coffee in the water then water in the coffee because some of that water was the original coffee that you put in the water.
That "trick" is commonly known as the "bat and ball problem". It's usually phrased as "A bat and a ball together cost 1.10, and the bat costs a dollar more than the ball. How much does the ball cost?" Almost everyone (including maths students) gets it wrong the first time they hear it. I think it was re-popularized in 'Thinking Fast & Slow'.
Ok I'm going to give this a try: So say the coffee is 99 units of coffee and the bottle of water is 99 units of water. A spoon is 1 unit. After transferring the coffee, the water has 99u of water and 1u of coffee. But then the spoonful we move back isn't pure water. It's 99% water and 1% coffee. So we add .99u of water back to the coffee. But we also have .99u of coffee in the water because 1% of it is in the second spoonful. So I guess, it's equal? Edit: I got it!
you added more coffee to the water than vice versa. you added a mix of water and coffee to the coffee so most of that spoonful was water but there was some coffee in there
My first intuition was right but I dismissed it and started to calculate the percentages of coffee and water and it got messy. The answer is incredibly simple. In the end, both the cups have equal amount of liquid in them. So, if the water cup has x amount of coffee in it, the missing x amount of water must be in the coffee cup. Because their weights are the same in the end. Simple.
the cost of the container and water is an old math trick. it was made famous in the book "Think Fast Think Slow" a ball and a bat cost $1.10 the difference is $1.00. people come up with the "fast" answer one is $1.00 other is $0.10 sum is $1.10 but difference is 90 cents when it should be $1.00 thereby the name of the book. leason is use algabra. A+B=1.1 A-B=1.0 I think algabra can be used for the mixing problem too.
So, Let's assume that there were about 10 spoons of water in one container and about 10 spoons of coffee in another container. Container 1= 10 water. Container 2= 10 coffee Let's take a spoon of coffee and put it into the water container Container 1= 10 water + 1 coffee. Container 2= 9 coffee Now lets take one spoon from the water container and put it into the coffee container. Container 1= 9+(1/11) water + (10/11) coffee Container 2= 9+(1/11) coffee +(10/11) water I hope that helps people visualise it.
The numbers are unnecessary. You can do all the mixing back and forth you want. In the end, because no coffee or water is created or destroyed, the percentages in the two cups must be reciprocal. If there is x% of liquid A in cup B, there must be x% of liquid B in cup A.
Let’s say 1/10th of the coffee’s volume was placed in the water. Now the water glass is 10 parts water and 1 part coffee, a 10:1 ratio. Now taking the same 1/10th scoop from the water, it will have that 10:1 ratio, but 11 parts total. So, 10/11ths of the 1/10th of the scoop is water, where 10/11 X 1/10 = 1/11, and 1/11th of the 1/10th scoop is coffee, where 1/11 X 1/10 = 1/110. This leaves 109/110th of the original 1/10th (109/1100) scoop of coffee in the water. Conclusion: There is 109/1100th (0.0991) of a scoop of coffee in the water and 1/11th (0.091) of a scoop of water in the coffee. There is more coffee in the water than water in the coffee.
thannk you idk why people arent seeing the fallacy. Whichever liquid you take from first is going to be the less dilute of the liquids in the end as you end up 'giving' some of that same liquid A back upon mixing.
"Now taking the same 1/10th scoop from the water" That's where you went wrong. You're not supposed to take 1/10th from that cup. You're supposed to take the same amount, which won't be 1/10th of the liquid that's in that cup.
It's counterintuitive, but it does not matter at all how many times you make the bi-transfer, or how well the liquids are mixed in the spoon. As long as the level of liquids remains the same, the *net result* of any bi-transfer - a certain amount of water was replaced with the exactly the same amount of coffee, and vice versa, in either cup.
Cool. Once he's sent over 3 coffee cards, it's like - when he us returning 3 cards you can think of it as 'a coffee card is undoing the coffee transfer' and 'a water card is making up for a coffee card'. That's genius. I'm gonna think about that now
This same principle works when multiplying percentages together. 10% and 28% when both multiplied to some amount results in the same number no matter which of the two percentages you apply first, and the same works in reverse.
This would be easier to understand if we were took a look at this in a common denominator. Like 6. If you took 3/6 of the coffee glass and added it to the water glass, the water glass would then have 2/6 coffee and 4/6 water. Now, when we return the same amount back to the coffee (3/6 of the original amount), the added mixture will add 1/6 coffee and 2/6 water to the coffee glass. This means we had the initial 3/6 of coffee that we left in the glass, added 1/6 of coffee and 2/6 of water. The water glass is now 2/6 (or 1/3 in lowest form) coffee while the coffee glass is also 1/3 water. I have spent way too much time thinking about this because initially it seemed obvious that there would be more coffee in the water than water in the coffee.
This video messed with my head, and I honestly didn't wrap my mind around the water/coffee trick until looking at the comments, and I didn't wrap my mind around the cards track until a few hours later. But I'll try to give my explanation here. The important thing to remember is that the quantity transferred is the same. Mass is conserved and liquids are incompressible, so volume is conserved. Therefore the problem is "path independent," a.k.a the end result won't change no matter what transfers and mixtures are performed. The path that it takes to get to the end does not matter. If glass A originally holds W ml of water and glass B originally holds C ml of coffee, what happens after two transfers? The volumes are equal, so initially W=C. If we let X be the total volume of water transferred in the end and Y be the total volume of coffee transferred in the end, now glass A holds (W-Y) ml water + X ml coffee, while glass B holds (C-X) ml coffee + Y ml coffee. Since we know that the glasses hold the same volume at the end, we can say that (W-Y)+X = (C-X)+Y. Regroup the Xs and Ys to get W+2X = C+2Y. Since neither water nor coffee can be created from thin air, the equation must balance to W=C in the end, and this is only possible if X=Y. Therefore, the amount of water transferred to the coffee glass is the same as the amount of coffee transferred to the water glass.
To put it simply any extra coffee transferred to the water glass is returned when the water is added to the coffee glass. It can't NOT be so. It's just a little strange to think about at first. Just like the 22 cents bit. My initial thought was the same as that guy, I knew it was wrong, but it was my initial thought. I had to actually stop and be like ok, if it costs 1 cent and the other thing costs 21, then.... I mean it didn't take long but still. The mind is funny like that sometimes. Our first instinct can be wrong. That is what this video, both examples, is trying to exemplify.
Assume you start with 100 parts coffee, in one container, and 100 parts water, int the other container. If in the final mixture one container has 39 parts coffee and 61 parts water, the other container has to have the 'missing' components from each of those parts, so 100-61=39 parts water and 100-39=61 parts coffee.
Fun fact, when you first poured a spoon of coffee into the water, the mixing part is unnecessary. You could have most of the coffee lying around in the edge and some of it mixed and the answer to the problem won't change.
That makes sense. The only way it will not be even if you took a spoonful of water out of the water glass first, then ad a spoonful coffee in to the water glass then transfer a spoonful of that water coffee mixture in to the coffee glass. Then ad that spoonful of water you took out of the water glass and put it back in the water glass. So the following must be true. If you took half of the coffee and poured it in to water glass and mixed it. Then transfer half of that mixture back in to the coffee glass, both of the containers should have exactly the same amount of the coffee/water mixture. It has to.
Here I was trying to answer the wrong question. The way it was phrased, I thought the question was about the two discrete transfers, not the final amounts remaining in each glass. That is, I was discounting the coffee transferred back to the coffee glass, because he only asked about water going in that direction.
I always thought it was simpler to think of it like this: if you imagine the ends of a seesaw, the distance between the floor and the seat represents the volume of liquid A, and the distance between the seat and the apex of the seesaw in the air represents the volume of liquid B. Now if you push down on the left side(lowering the volume of liquid A and increasing the volume of liquid B in the left glass), the right side of the seesaw will rise an equal amount(increasing the volume of liquid A and decreasing the volume of liquid B in the right glass by an equal amount). Therefore if you remove or add one liquid, it must be replaced on the other side by an exactly equal amount of the other liquid, otherwise the seesaw would need to bend in our analogy.
Actually the answer is that you've added more coffee to the water than you added water to the coffee. You added a full spoon of coffee to the water but you did not add a full spoon of water to the coffee. It is also true that they have the exact equal amount of each in the end.
They actually both gave away the same ammount: Lets assume we have 10ml of water and 10ml of coffee, you take 1ml of 100% concentrated coffee and put in the water, now the water has 11ml, 1/11 beeing coffee, so 9% coffee and 91% water, so when you give a spoon from the water back to the coffee you actually have 91% water and 9% coffee, so u get 9% back from the 100% you originally gave away so u actually gave 91%, just like the water u got.
@@NjoyMoney as I said, in the end you have the same amount of water in the coffee as you have coffee in the water. That's because they started as equal amounts of total liquid and ended as equal amounts of total liquid, and whatever is missing from one has to be displacing that exact amount in the other. But his question was have you added more of one to the other than vice versa? Yes you added more coffee to the cup of water. A spoon full. You then added water and coffee to the coffee cup. And the amount of water in that spoon was not a spoon full. So it's true that you added more coffee to the cup of water than you added water to the coffee cup. You then have to figure in the amount of coffee subtracted from the water cup and put back into the coffee cup, but that part wasn't mentioned in the question. Also. The coffee is mostly water and as soon as you put coffee in the water it became coffee which invalidated the rest of the experiment.
its clear as day that he added More coffee than he added More water, as he asked. since he did Not take a spoonful Before he mixed, there is more coffee. easy science even for 1980
All other things being equal, this works only if both of them are equal dense and mix well together. I believe that coffee is ever so slightly more dense than Water, so it will sink to the bottom quicker, so the resulting liquid of water and coffee is not perfectly mixed.
The density is irrelevant. Assume each glass contains 100ml of liquid and 10ml of coffee is transferred to the water glass. Imagine it immediately sinks to the bottom. Then 10ml is transferred from the top of the water glass to the coffee glass. Both glasses contain 100ml of liquid again, and exactly 10ml of coffee ended up in the water glass and 10ml of water ended up in the coffee glass, thus matching the claim that the same amount of each substance was moved.
Ah, that was easy. Can you spoon the liquid back and forth to make both solutions have the exact same percentages of water and coffee? Is it possible, and if, what algorythm would you use?
@goohz has a channel Obviously there's a glass limit. But when are both solutions the same? And why? Btw, you cannot shift infinitely. You're still human. Drinking is not part of the game either.
Surprising result... I originally expected more coffee to be added to the water. I'm sure the card analogy won't work all the time. Here's the working: Lets say there are N units of coffee and N units of water in each respective cup, a 'unit' being defined as the volume of liquid which occupies the measuring spoon. One unit moves to the water glass, there are now N+1 units in this glass: N units of water and 1 unit of coffee. One unit of from the water glass is then removed... this is equal to 1/(N+1) of the total mixture... so in the spoon, there will be N/(N+1) units of water, and 1/(N+1) units of coffee. Note that these quantities add up to 1 unit, as expected. We won't add this to the coffee glass yet, instead, we'll look at what is left in the water glass. In the water glass, there is now: 1-1/(N+1) = (N+1 - 1)/(N+1) = N/(N+1) units of coffee and N-N/(N+1) units of water.... these add together to give a total of N units in the water glass, as you'd expect. Notice that the amount of water in the spoon we add to the coffee is N/N+1, which is equal to the quantity of coffee left in the water.
Indeed, the card trick works every time, by this logic: You have two stacks of N cards. You take k cards from stack A and put them into stack B. At this point, stack B has N cards and k cards from A. You take k cards from stack B and put them into stack A. You will either: - take k cards that were originally from A and put them into B - take (k-1) cards [as above] + 1 card from B into A - take (k-2) cards [as above] + 2 card from B into A ... - take k cards from B into A. Let's call the number of cards that go back and forth d, so now A will contain: n cards that were originally in A -k cards that went to B +[k-d] cards that were originally in B +d cards that were in A then B then A while B will contain: n cards that were originally in B +k cards that were originally in A -[k-d] cards that were originally in B and went to A -d cards that were in A then B than A so A contains n-k*d cards from A, and k-d cards from B and B contains n-k+d cards from B and k-d cards from A
Imteresting. On the second transfer from water cup back to coffee cup you're either equalising the coffee:water ratio by transferring water to coffee, or undoing some of your original coffee transfer. You could theoretically return all the coffee back - and you'd have Equal-Amounts. You could return only water and have Equal Amounts. Anywhere in between will give you a result of something between Equal-Amounts and-Equal Amounts
Yeah, you guys are right, the card trick does work every time, I was being a brainlet... Actually, the card analogy better describes what's going on, because it's discrete, rather than continuous. With the water/coffee I was thinking about it in terms of continuous units (based on probability and full diffusion etc). The card case shows that even if you didn't stir the water/coffee, you'd still transfer the same back and forth.
A) at the end, there is the same amount of liquid in each container. B) composition of both liquids changed from initial state, but it is not really a question being asked. Just adding concept of diffusion into the mix - once you add coffee (coffee water) into pure water, you will get diluted mix. Separating coffee from water would probably be possible using only using distillation and probably (oils etc.) via centrifugal separation. Definitely not mechanically possible. But that was not the question, anyways.
He put a spoon of 'pure coffee' into the water, but returned a spoon of coffee/water mixture. I'd say a tinge more coffee ended up on the water than water returned to the coffee.
This is why da universe isnt just math lol...now take a sip of the coffee and ul taste coffee...but take a sip of da water and it wont taste like water
Thanks. Curiosity Show was a national science program featuring Dr Rob Morrison and Dr Deane Hutton. It was made in Adelaide, South Australia and screened nationally in Australia as well as in Europe, Asia and Australasia (14 countries and dubbed in German for Europe) from 1972-1990. Deane and Rob intentionally used everyday items around the house (like old rusty cans) so that people could repeat the demonstrations with materials they had to hand. In 1984 Curiosity Show won the Prix Jeunesse International, the world's top award for TV programs for young people. Rob and Deane are steadily uploading segments at th-cam.com/users/curiosityshow Why not subscribe?
Notice that mixing is not even necessary. Fixing the volume taken by the spoon is the only condition needed to guarantee that there is the same amount of coffee in water as there is of water in coffee. In a microcanonical perspective: their entropies are the same (:
But steel is heavier than feathers
I dont quite understand
1 kg steel has the same weight than 1kg feathers.
However when someone asks, ‘Which is heavier, a pound of feathers or a pound of gold?’ do not say they’re the same because they’re not!
Feathers are measured in avoirdupois weight at 16 ounces to the pound - gold is measured in troy weight at 12 ounces to the pound 🧐
Hahahahahhaha
Thanks Limmy
I love that the information is often presented as a couple of buddies trying to outwit each other. I really think it makes the concepts appeal more to younger people especially young boys.
Competition is also great for progress and learning. Watching 2 people play catch? Neat. Monkey in middle? Now ya get to see how people get out of the middle
I'm not sure if I'd want them to pull out a pack of card or matches if having a coffee with them. I'd like the opportunity to arise though. 😀
is steel heavier than feathers though
@@BigLee93 Per unit of volume, yes it is
I bet very few girls watched this show. You can see this on TH-cam as well. Videos on math and science clearly get almost exclusively comments by men or boys. Women seem to be much more interested in other stuff, like ... well I don't know. (Pets? Makeup?)
For those who want to math it out:
If each cup has 90ml, and you transfer 10ml from the coffee cup to the water cup, then the water cup will have a 100ml mixture of 10/90 coffee/water ratio. Meaning that 10ml of this mixture would consist of 1ml coffee and 9ml water. Removing that 10ml from the water cup would leave only 81ml water and 9ml coffee.
If you then transfer that 10ml back to the now 80ml of coffee, then the coffee cup will have 90ml again, but will only 81ml of it will be coffee and 9ml of water.
There is exactly as much water in the coffee cup as there is coffee in the water cup. That’s all this experiment was trying to demonstrate.
m is proportion removed. water glass proportion is 1/(1+m). coffee glass proportion is 1-m+m(m/(1+m))=(1-m^2+m^2)/(1+m)=1/(1+m)
Well, the thing is that you have explained the case where the mixture is perfect. It is a special case. What was shown with the deck of cards was that it works in the general case where the mixture is not perfect as well.
@@Sauromannen In the case of the cards and the liquids, it is the same because:
1. The quantity of each type of liquid/card is conserved
2. The same amount of liquid/cards is in each glass/hand.
The same quantity of each liquid has been moved from each glass to the other because the same quantity of the other liquid must be moved the other way to replace it to keep the water level. If you always have 10 cards in each hand, and there are 10 cards of each type (face up and down), then if there are 2 face up cards in your deck (thus 8 face down cards), then there must be 8 face up cards in the other deck (thus 2 face down).
@@styraco4739 you did not understand my point. The mixture of the liquid does not have to be as shadowstalker or Katherine showed. They are not wrong but show only the special case where the mixture is perfect. It does not have to be perfect as can be illustrated by the card example.
@@styraco4739 In reality there's no way to know if you grabbed the same amount, unless the substance is perfectly homogenized and you are indeed capable of grabbing the exact same amount and there was no loss of liquid in the transfer. There always is and it doesn't matter for real world purposes but if you're showing scientific exactness it does need to be accounted for in the equation. The card example works but the liquids do not. There's roughly the same amount but that's really the best you can say.
What made it click for me was thinking about the maximum and minimum limits with the card example. Remember, the question was about the final ratio of water to coffee being equal in each cup (or deck), regardless of the amount. After the initial three cards went into the "water deck" and it was shuffled, he said you can choose any three cards to put back in the "coffee deck." So what if we chose 3 "coffee cards"? OK. The ratio would be back to the starting amount, yes, BUT it is equal, as the same amount (zero) has been transferred. If you chose 3 water cards to put back then there would be three water cards in the coffee deck and those three original coffee cards left in the water deck. Equal.
Well done sir. Elon Musk is hiring.
There is a semantic argument, with the phrasing "have I added more of coffee to the water cup or more of water to the coffee cup" is imprecise. But the real answer is so much cooler!
@@CycleMantis The biggest semantic issue here is that there is already more water in the coffee than actual coffee. So one could say that you swapped equal amounts of each glass, but not necessarily equal amounts of coffee and water. The play might work better with something like coffee and milk.
@@patrickkeller2193 no, that's incorrect, it's beside the point what solutions you have in each glass to start with, after the final transfer you'll have the same ratio in each glass. even if the coffee solution is in fact 75% water, the end result will be the same ratio of water/coffee in both glasses. as long as the fluids you are using are soluble and mixed evenly this equation will work with any substance.
@@cool_bug_facts why not? He's looking into future tech and future energy. So tell me what I'm missing
Brilliant.
The use of cards to demonstrate is the simplest explanation I've ever seen for this puzzle
It was actually pretty dumb, because you won't always randomly pick the same cards, so there is probability involved, where in the liquid there is not.
@@blindi6326 The liquids are made of molecules which move around in the glasses more or less randomly. Probably more randomly than card shuffling. So it's actually a perfect analogy. Maybe go back to school before calling people dumb?
@@coryc9040 that is the dumbest shit I have heard this week
@@blindi6326 the point is, you don't have to randomly pick specific cards. It works with any amount of cards, and any sized bunch of cards. The only requirement is that the amount you switch is the same both ways. So you could do it with 21 card deck, take 8 from one side over to the other, then take 8 back. Doesn't matter which 8 you choose for the return, it will always end up with equal amounts switched. So 8 coffee over and 8 coffee-0 water back, 7-1 back, 6-2 back, 5-3 back, no matter which 8 cards you send back there will ALWAYS be equal representation. That's the point.
@@blindi6326 but with his example in the video, if you brought all 3 coffee cards back then there's be zero opposite cards on each side. If you bring two coffee card back there'd be one opposite card on each side. If you bring one coffee card back, there'd be two opposite cards on each side. If you bring zero coffee cards back there'd be three opposite cards on each side. No matter what you do, the mixes stay exactly opposite with the same amount of the other card left.
Dude… where has this show been my whole life??? I love it!
My childhood. Ahh, intelligent children's tv programming.
Well you are watching them now. And perhaps you can now share them with your kids.
In Australia. Those darn Aussies were holding back from the rest of the world.
I loved these segments as a kid... kept me glued to the telly for 29 minutes straight... without blinking. 👀 Kerry Packer must've loved you guys 👍
Well, Channel Nine kept us on for 18 years, so it was good for all of us - Rob
What a show. My favourite of all through my childhood
Magician here: For anyone interested in learning the actual card trick this relates to the routine is commonly known as the "Oil and Water" card trick and there's probably dozens of demonstrations on how to learn and perform the trick. It's a classic of card magic and a fun, interesting and self working routine that will have your spectators completely astounded. Enjoy.
Why is your name really furious?
You seem like a nice enough fella... 😕
@@AksTube it's a play on words for the game which my channel is about. The game is called Rally Fury and when you get frustrated playing it you get Really FURIOUS.
@@reallyfurious Thanks. I'm gonna check it out ☺️
This show should still be in the tv to teach curiosity to our youngsters!!!
The cards are a very helpful way to understand the bottom line of this problem. If there was more coffee in the water glass than water in the coffee glass and both glasses had equal volumes, we would be asking what happened to the missing water!
But wouldn't the playing cards ger stained by the coffee?
Larry! You always seem to pop up in the comments of the most obscure videos. Great minds really do think alike.
The coffee conundrum doesn't quite make sense to me.
Nevermind, I got my fractions on the water side wrong
SERIOUSLY?
Watch it again - it makes sense when you think about it the right way - Rob
crapstirrer I sympathise. Take ten red cards and ten black cards, mix them up and separate into two piles of ten. If one has 7 to 3 then the other must have 3 to 7. I guess you don't have a problem with that. Maybe your problem is how this is analogous to the dilution of coffee? Me too. It isn't. Starting from a glass of salt water and a glass of pure water we know that salt water is denser, it contains more matter per unit volume. So the first transfer by volume carries more matter than the second.. The transfer is equal by volume but not by mass. The answer given is right if the judgement is by volume but wrong if it's by mass. So the question asked is vague. Don't get me wrong, as a 63 year old child physicist I adore this channel !
Ray Kent sir I’m like you, but if you’re putting pure coffee into water, then that mixture back into coffee the water is diluted, ohhhh I see.
I would have loved this show as a kid. That's ok, I can enjoy it now!
My wife probably wonders what I watch on my phone…
Me: Curiosity Show.
I dont get it,
The coffee diffuses into the water, so per u it volume, less coffee will be transfered back into the coffee cup no?
not exactly. according to the law of conservation of mass as long as the same amount of matter is in both cups, the ratio will be the same between them. You can't have more coffee in one cup when the same amount of water needs to be in the other cup to keep the balance.
Because you have taken away a spoonful of coffee to begin with there is less coffee in the cup before you return the water/coffee solution to the coffee cup.
Exactly correct
Yes. There will be less coffee in the coffee and less water in the water than there was in the beginning. But- the same amount of water will be in the coffee as coffee in the water.
Yes! But that's not what the question was. It was if more water went to the coffee cup or if more coffee went to the water cup.
This is great. Thank you, from a 51 year old engineer!
This show is a gem
Look at it this way : The first spoonful is 100% coffee , the second spoonful is now less than 100% water but is now added back to a lesser volume of coffee . So the coffee/water ratios remain exact opposites from one glass to the other until they are both 50/50 .
That's a great ad infinitum explanation. If you transfer back and forth an infinite number of times, they'll both be equal. Therefore the ratios getting discussed must have always been equal.
Indeed. If you do it often enough, at some point the ratio would be 50:50 in both glasses.
But the second spoonful from the water isnt all water. This doesnt make any sense. The cards are a bad example as they arent a homogenous solution they are separate entities. The water and coffee become the same solution
@@yeelahowah7476 I thought it through last night. The way I finally understood was more coffee in more water=Less water in less coffee. Idk if that makes sense to you
I finally understand it now, thank you good sir
It works with cards but it's not the same. Spoon of 100% coffee goes in, spoon of maybe 5% coffee comes back.
The question itself is what’s confusing. The conclusion is just saying that both cups have 95% of one thing and 5% of the other. Well, duh.
That said, “pure coffee” is itself mostly water 🤔
What an amazing puzzle! Or is it a conundrum? I guess both? Anyway, firstly, the question is a bit poorly worded. What they asked is "have I added more of this (coffee & water mixture) into this, or this (water and coffee mixture) into that? Well, you added more coffee into the water cup, but you also took out some coffee of that cup later.
However, the question is intended to be "is there more water in the coffee cup, or more coffee in the water cup - or are these quantities the same?" To this, the answer is that they are the same, _regardless of whether you mix properly after the scoop._ You could do this with cards, shuffle them randomly, and it always works. This is because the remaining coffee in the water cup will be 1 - (the amount of coffee you transfer back with the second scoop), where "1" is the full original scoop, and the water in the coffee scoop is 1 - (the amount of coffee you transfer back with the second scoop), where 1 is the full second scoop, but the second term is however much of that scoop is occupied by the coffee you had just put in there. You can see that these two terms are the exact same!
The paradoxical or counter-intuitive feel of the puzzle comes from the fact that we mostly think "we just put a full cup of coffee in the water cup, and we only put slightly less water back in the coffee cup". However, this fails to account for the fact that when you take the coffee to the water, it's 100% coffee, while if you take some water to the coffee, you just fill the remaining part up with coffee you had just transferred. Less water means more coffee at the exact same rate, as shown above! So you put more coffee into the water cup, but you never took any water back to the water cup. You did, however, put coffee back into the coffee cup - exactly the difference between how much coffee you put into the water, and water into the coffee.
So hopefully, that not only provides a solution / "proof" to the problem, but also one that is intuitive, along with an explanation of exactly where most people go wrong in their thinking and why. I originally got this wrong because of the flawed reasoning I described above, and I find it incredibly interesting to find out how my mind can be so easily tricked. Hope y'all do too.
If it's a closed system, and assuming the 2 cups have equal levels of fluid, the fluids can only exchange places in equal amounts.
"Will the ratio of water to coffee in this glass be the same as the ratio of coffee to water in this glass?" That was the question. That was the point.
What are the best bits of the show? I'm glad u asked. It's when they pretend to be dumb
Try it on your friends!
Cards and water are different. If you put coffee in the water now the water is no longer 100% water. perhaps it's 90% water and 10% coffee. Now you take a scoop of what is only 90% water and 10% coffee and you pour it back into the coffee. You have poured 10/10 of coffee into water but you have only returned 9/10 of water into the coffee. Therefore you put more coffee in the water then water in the coffee because some of that water was the original coffee that you put in the water.
Me yelling at the screen.
*No, you're wrong, your wrong, y--- oooh. I see*
I like how he added a completely non-related price problem in the beginning. And I admit I screwed up.
That "trick" is commonly known as the "bat and ball problem". It's usually phrased as "A bat and a ball together cost 1.10, and the bat costs a dollar more than the ball. How much does the ball cost?"
Almost everyone (including maths students) gets it wrong the first time they hear it. I think it was re-popularized in 'Thinking Fast & Slow'.
He wasn’t asking what glass has more liquid. He was asking was there more coffee in the water cup or more water in the coffee cup
This show is effin' amazing!
This is so freaking calming wow
Those glasses are iconic.
Man I can feel by brain leveling up from figuring that math out on this. Super cool.
Ok I'm going to give this a try:
So say the coffee is 99 units of coffee and the bottle of water is 99 units of water. A spoon is 1 unit. After transferring the coffee, the water has 99u of water and 1u of coffee. But then the spoonful we move back isn't pure water. It's 99% water and 1% coffee. So we add .99u of water back to the coffee. But we also have .99u of coffee in the water because 1% of it is in the second spoonful. So I guess, it's equal?
Edit: I got it!
As liquid weight/mass YES... as particulate matter... NO (coffee is not a liquid but disolved in it - They needed to phrase the question better IMO)
@@dracael it was intended for kids in the 1980’s, not chemistry undergrads in the 2020’s
water was already in the cofee, but water was pure. so we contaminated water with coffee but only added more water to the coffee
@@mjhobo5520 No shit sherlock..., i was one of those kids that watched this in the 80's!
@@dracael, well done you
you added more coffee to the water than vice versa. you added a mix of water and coffee to the coffee so most of that spoonful was water but there was some coffee in there
I used to race home from school for the Curiosity Show...great part of my growing up. Wish my kids have stuff like this nowadays.
Many thanks, make sure they subscribe at th-cam.com/users/curiosityshow - Rob
My first intuition was right but I dismissed it and started to calculate the percentages of coffee and water and it got messy.
The answer is incredibly simple.
In the end, both the cups have equal amount of liquid in them. So, if the water cup has x amount of coffee in it, the missing x amount of water must be in the coffee cup. Because their weights are the same in the end. Simple.
This clears up a lot that I missed in high school.
Dilutions have always been mind bending to me
That's some weak looking coffee
both look weak :)
I’m just tripping over the fact that this quality bottle with glass stopper included is merely 22¢
the cost of the container and water is an old math trick. it was made famous in the book "Think Fast Think Slow" a ball and a bat cost $1.10 the difference is $1.00. people come up with the "fast" answer one is $1.00 other is $0.10 sum is $1.10 but difference is 90 cents when it should be $1.00 thereby the name of the book. leason is use algabra.
A+B=1.1
A-B=1.0
I think algabra can be used for the mixing problem too.
algebra*
Man...70s Australian water is... cloudy.
Right, because playing cards dilute in water. Being upside down all their lives must have played havoc with their brains.
Yep. Beautiful simple stuff
I wish things like this were still on tv
Does anyone know where to find more questions like this?
When I was kid in the 80s there was just no other show like this. Half the stuff we use to make at school we saw on the Curiosity show.
While the trick works, my question is: how does it work?
So I’m the only one that saw he grabbed 4 cards the first time?
So,
Let's assume that there were about 10 spoons of water in one container and about 10 spoons of coffee in another container.
Container 1= 10 water. Container 2= 10 coffee
Let's take a spoon of coffee and put it into the water container
Container 1= 10 water + 1 coffee. Container 2= 9 coffee
Now lets take one spoon from the water container and put it into the coffee container.
Container 1= 9+(1/11) water + (10/11) coffee
Container 2= 9+(1/11) coffee +(10/11) water
I hope that helps people visualise it.
The numbers are unnecessary. You can do all the mixing back and forth you want. In the end, because no coffee or water is created or destroyed, the percentages in the two cups must be reciprocal. If there is x% of liquid A in cup B, there must be x% of liquid B in cup A.
Let’s say 1/10th of the coffee’s volume was placed in the water. Now the water glass is 10 parts water and 1 part coffee, a 10:1 ratio. Now taking the same 1/10th scoop from the water, it will have that 10:1 ratio, but 11 parts total. So, 10/11ths of the 1/10th of the scoop is water, where 10/11 X 1/10 = 1/11, and 1/11th of the 1/10th scoop is coffee, where 1/11 X 1/10 = 1/110. This leaves 109/110th of the original 1/10th (109/1100) scoop of coffee in the water.
Conclusion: There is 109/1100th (0.0991) of a scoop of coffee in the water and 1/11th (0.091) of a scoop of water in the coffee.
There is more coffee in the water than water in the coffee.
thannk you idk why people arent seeing the fallacy. Whichever liquid you take from first is going to be the less dilute of the liquids in the end as you end up 'giving' some of that same liquid A back upon mixing.
"Now taking the same 1/10th scoop from the water"
That's where you went wrong. You're not supposed to take 1/10th from that cup. You're supposed to take the same amount, which won't be 1/10th of the liquid that's in that cup.
Good one! Could have never guessed
It's counterintuitive, but it does not matter at all how many times you make the bi-transfer, or how well the liquids are mixed in the spoon.
As long as the level of liquids remains the same, the *net result* of any bi-transfer - a certain amount of water was replaced with the exactly the same amount of coffee, and vice versa, in either cup.
Took a bit but i got it. Well done.
Cool. Once he's sent over 3 coffee cards, it's like - when he us returning 3 cards you can think of it as 'a coffee card is undoing the coffee transfer' and 'a water card is making up for a coffee card'. That's genius. I'm gonna think about that now
Its cool that there was less water left over.
This same principle works when multiplying percentages together. 10% and 28% when both multiplied to some amount results in the same number no matter which of the two percentages you apply first, and the same works in reverse.
can you give an example please ?
That first math example took me way too long to comprehend lol 🤦♂️.
I was tricked. How neat, and simple :p
And humbling, ha.
He added pure coffee to the other glass and replaced it with coffee water
This show ended when I was 3 yrs old. I don't remember it at all, but it's a great show and worthy of still being on TV.
This would be easier to understand if we were took a look at this in a common denominator. Like 6. If you took 3/6 of the coffee glass and added it to the water glass, the water glass would then have 2/6 coffee and 4/6 water. Now, when we return the same amount back to the coffee (3/6 of the original amount), the added mixture will add 1/6 coffee and 2/6 water to the coffee glass. This means we had the initial 3/6 of coffee that we left in the glass, added 1/6 of coffee and 2/6 of water. The water glass is now 2/6 (or 1/3 in lowest form) coffee while the coffee glass is also 1/3 water. I have spent way too much time thinking about this because initially it seemed obvious that there would be more coffee in the water than water in the coffee.
Lmao this is definitely not an easier to understand way of communicating this.
I think Deane is playing dumb here. 😂
Did the thing with the cards blindfolded and somehow put back all the coffee cards into the coffee stack
Nope. Take a lap.
This video messed with my head, and I honestly didn't wrap my mind around the water/coffee trick until looking at the comments, and I didn't wrap my mind around the cards track until a few hours later. But I'll try to give my explanation here.
The important thing to remember is that the quantity transferred is the same. Mass is conserved and liquids are incompressible, so volume is conserved. Therefore the problem is "path independent," a.k.a the end result won't change no matter what transfers and mixtures are performed. The path that it takes to get to the end does not matter.
If glass A originally holds W ml of water and glass B originally holds C ml of coffee, what happens after two transfers? The volumes are equal, so initially W=C. If we let X be the total volume of water transferred in the end and Y be the total volume of coffee transferred in the end, now glass A holds (W-Y) ml water + X ml coffee, while glass B holds (C-X) ml coffee + Y ml coffee.
Since we know that the glasses hold the same volume at the end, we can say that (W-Y)+X = (C-X)+Y. Regroup the Xs and Ys to get W+2X = C+2Y. Since neither water nor coffee can be created from thin air, the equation must balance to W=C in the end, and this is only possible if X=Y. Therefore, the amount of water transferred to the coffee glass is the same as the amount of coffee transferred to the water glass.
To put it simply any extra coffee transferred to the water glass is returned when the water is added to the coffee glass. It can't NOT be so. It's just a little strange to think about at first. Just like the 22 cents bit. My initial thought was the same as that guy, I knew it was wrong, but it was my initial thought. I had to actually stop and be like ok, if it costs 1 cent and the other thing costs 21, then.... I mean it didn't take long but still. The mind is funny like that sometimes. Our first instinct can be wrong. That is what this video, both examples, is trying to exemplify.
Assume you start with 100 parts coffee, in one container, and 100 parts water, int the other container. If in the final mixture one container has 39 parts coffee and 61 parts water, the other container has to have the 'missing' components from each of those parts, so 100-61=39 parts water and 100-39=61 parts coffee.
I know it’s right, but MIND BLOWN! 😁👍 I was *so* convinces there was more coffee as some of the coffee went back with the water. lol
aye
I really like this one
Fun fact, when you first poured a spoon of coffee into the water, the mixing part is unnecessary. You could have most of the coffee lying around in the edge and some of it mixed and the answer to the problem won't change.
Coffee and water aren't cards... water dilutes the coffee. Then you add the diluted coffee back into the water
That makes sense.
The only way it will not be even if you took a spoonful of water out of the water glass first, then ad a spoonful coffee in to the water glass then transfer a spoonful of that water coffee mixture in to the coffee glass. Then ad that spoonful of water you took out of the water glass and put it back in the water glass.
So the following must be true. If you took half of the coffee and poured it in to water glass and mixed it. Then transfer half of that mixture back in to the coffee glass, both of the containers should have exactly the same amount of the coffee/water mixture. It has to.
Whatever ratio is in cup A the inverse ratio is in cup B since the volumes are equal.
Here I was trying to answer the wrong question. The way it was phrased, I thought the question was about the two discrete transfers, not the final amounts remaining in each glass. That is, I was discounting the coffee transferred back to the coffee glass, because he only asked about water going in that direction.
What are some of the cards tricks that are supposedly based on this principle?
I always thought it was simpler to think of it like this: if you imagine the ends of a seesaw, the distance between the floor and the seat represents the volume of liquid A, and the distance between the seat and the apex of the seesaw in the air represents the volume of liquid B. Now if you push down on the left side(lowering the volume of liquid A and increasing the volume of liquid B in the left glass), the right side of the seesaw will rise an equal amount(increasing the volume of liquid A and decreasing the volume of liquid B in the right glass by an equal amount). Therefore if you remove or add one liquid, it must be replaced on the other side by an exactly equal amount of the other liquid, otherwise the seesaw would need to bend in our analogy.
simpler...
Good visualization of difference of volume vs concentration
Ahhh, to be back to the days when television was educational and people believed in logic and science.
Back when actual science was demonstrated on tv and it wasn't just a picture of people with test tubes and politicians being tauted as scientists.
I could go for a glass of watered down coffee
Uncle Rico never was too good at math
Does this work with chocolate and peanut butter?
You keep your damn chocolate out of my peanut butter !
YUP!
These guys remind me of a discount Hall & Oates
Hall & Oates is really just discount Rob & Dean 😝
Actually the answer is that you've added more coffee to the water than you added water to the coffee. You added a full spoon of coffee to the water but you did not add a full spoon of water to the coffee. It is also true that they have the exact equal amount of each in the end.
Thank you i did not want to type that out lol
They actually both gave away the same ammount:
Lets assume we have 10ml of water and 10ml of coffee, you take 1ml of 100% concentrated coffee and put in the water, now the water has 11ml, 1/11 beeing coffee, so 9% coffee and 91% water, so when you give a spoon from the water back to the coffee you actually have 91% water and 9% coffee, so u get 9% back from the 100% you originally gave away so u actually gave 91%, just like the water u got.
@@NjoyMoney you don't understand
Numbers dont lie, nice explanation btw.
@@NjoyMoney as I said, in the end you have the same amount of water in the coffee as you have coffee in the water. That's because they started as equal amounts of total liquid and ended as equal amounts of total liquid, and whatever is missing from one has to be displacing that exact amount in the other. But his question was have you added more of one to the other than vice versa? Yes you added more coffee to the cup of water. A spoon full. You then added water and coffee to the coffee cup. And the amount of water in that spoon was not a spoon full. So it's true that you added more coffee to the cup of water than you added water to the coffee cup. You then have to figure in the amount of coffee subtracted from the water cup and put back into the coffee cup, but that part wasn't mentioned in the question. Also. The coffee is mostly water and as soon as you put coffee in the water it became coffee which invalidated the rest of the experiment.
its clear as day that he added More coffee
than he added More water, as he asked.
since he did Not take a spoonful Before he mixed,
there is more coffee. easy science even for 1980
But, probability tells me, he could have easily dealt cards that weren't applicable to the equation, then what?
My conundrum is why is the vid quality on this a show that ended in the nineties better than half the HD or 4k vids that are being made these days
All other things being equal, this works only if both of them are equal dense and mix well together.
I believe that coffee is ever so slightly more dense than Water, so it will sink to the bottom quicker, so the resulting liquid of water and coffee is not perfectly mixed.
The density is irrelevant. Assume each glass contains 100ml of liquid and 10ml of coffee is transferred to the water glass. Imagine it immediately sinks to the bottom. Then 10ml is transferred from the top of the water glass to the coffee glass. Both glasses contain 100ml of liquid again, and exactly 10ml of coffee ended up in the water glass and 10ml of water ended up in the coffee glass, thus matching the claim that the same amount of each substance was moved.
Instructions unclear: I had to get the glasses surgically removed from my lower intestine.
Ah, that was easy.
Can you spoon the liquid back and forth to make both solutions have the exact same percentages of water and coffee?
Is it possible, and if, what algorythm would you use?
@goohz has a channel
Obviously there's a glass limit.
But when are both solutions the same? And why?
Btw, you cannot shift infinitely. You're still human. Drinking is not part of the game either.
Surprising result... I originally expected more coffee to be added to the water. I'm sure the card analogy won't work all the time. Here's the working:
Lets say there are N units of coffee and N units of water in each respective cup, a 'unit' being defined as the volume of liquid which occupies the measuring spoon. One unit moves to the water glass, there are now N+1 units in this glass: N units of water and 1 unit of coffee.
One unit of from the water glass is then removed... this is equal to 1/(N+1) of the total mixture... so in the spoon, there will be N/(N+1) units of water, and 1/(N+1) units of coffee. Note that these quantities add up to 1 unit, as expected. We won't add this to the coffee glass yet, instead, we'll look at what is left in the water glass.
In the water glass, there is now: 1-1/(N+1) = (N+1 - 1)/(N+1) = N/(N+1) units of coffee and N-N/(N+1) units of water.... these add together to give a total of N units in the water glass, as you'd expect.
Notice that the amount of water in the spoon we add to the coffee is N/N+1, which is equal to the quantity of coffee left in the water.
Owl the card analogy will work all the time. What makes you think it won’t?
Indeed, the card trick works every time, by this logic:
You have two stacks of N cards.
You take k cards from stack A and put them into stack B.
At this point, stack B has N cards and k cards from A.
You take k cards from stack B and put them into stack A.
You will either:
- take k cards that were originally from A and put them into B
- take (k-1) cards [as above] + 1 card from B into A
- take (k-2) cards [as above] + 2 card from B into A
...
- take k cards from B into A.
Let's call the number of cards that go back and forth d, so now A will contain:
n cards that were originally in A
-k cards that went to B
+[k-d] cards that were originally in B
+d cards that were in A then B then A
while B will contain:
n cards that were originally in B
+k cards that were originally in A
-[k-d] cards that were originally in B and went to A
-d cards that were in A then B than A
so A contains n-k*d cards from A, and k-d cards from B
and B contains n-k+d cards from B and k-d cards from A
Imteresting. On the second transfer from water cup back to coffee cup you're either equalising the coffee:water ratio by transferring water to coffee, or undoing some of your original coffee transfer. You could theoretically return all the coffee back - and you'd have Equal-Amounts. You could return only water and have Equal Amounts. Anywhere in between will give you a result of something between Equal-Amounts and-Equal Amounts
Yeah, you guys are right, the card trick does work every time, I was being a brainlet... Actually, the card analogy better describes what's going on, because it's discrete, rather than continuous. With the water/coffee I was thinking about it in terms of continuous units (based on probability and full diffusion etc). The card case shows that even if you didn't stir the water/coffee, you'd still transfer the same back and forth.
@@FlavourlessLife yeah good point owl. Hoo hoo hoo
Since each cup has net 0 loss of liquid, it's equal.
Genius!
A) at the end, there is the same amount of liquid in each container.
B) composition of both liquids changed from initial state, but it is not really a question being asked.
Just adding concept of diffusion into the mix - once you add coffee (coffee water) into pure water, you will get diluted mix. Separating coffee from water would probably be possible using only using distillation and probably (oils etc.) via centrifugal separation. Definitely not mechanically possible. But that was not the question, anyways.
Yes I'm sure all the kids would love a good chat on distillation and centrifugal separation
I agree, it's one of those stupid puzzles that really doesn't relate to anything important, and all the wrong questions are being asked about it.
@@austingeorge6659 Probably more of an early learning thing, no? Thankfully, this isn't a college lecture on fluid mechanics.
@@cjonh808 lol the first day of my thermodynamics class this was shown except in our example it was water and wine
@@cane870 What I am saying is that bringing thermodynamics etc into the mix is only going to make it difficult to follow. Good bye
He put a spoon of 'pure coffee' into the water, but returned a spoon of coffee/water mixture. I'd say a tinge more coffee ended up on the water than water returned to the coffee.
That would mean there has to be more liquid in the water glass, which won't be the case if you just move exactly a spoonful from each glass.
But coffee is already mostly water in the first place 🤔
This is why da universe isnt just math lol...now take a sip of the coffee and ul taste coffee...but take a sip of da water and it wont taste like water
yes but now the water is a ratio of water and coffee so youre putting some coffee back in the coffee when you scoop it from the water
How did they have a math and science TH-cam channel before TH-cam existed?
Thanks. Curiosity Show was a national science program featuring Dr Rob Morrison and Dr Deane Hutton. It was made in Adelaide, South Australia and screened nationally in Australia as well as in Europe, Asia and Australasia (14 countries and dubbed in German for Europe) from 1972-1990. Deane and Rob intentionally used everyday items around the house (like old rusty cans) so that people could repeat the demonstrations with materials they had to hand. In 1984 Curiosity Show won the Prix Jeunesse International, the world's top award for TV programs for young people. Rob and Deane are steadily uploading segments at th-cam.com/users/curiosityshow Why not subscribe?
It's a deconstructed long-black.
Notice that mixing is not even necessary. Fixing the volume taken by the spoon is the only condition needed to guarantee that there is the same amount of coffee in water as there is of water in coffee.
In a microcanonical perspective: their entropies are the same (:
at first it seems counterintuitive but yea its actually correct because the second glas loses the spoon unit that later gets added back
i like to think that these two are older ActionLab and NileRed who timetravelled to the past because of a machine they made for a youtube collab