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/sci/ - Science & Math

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3989313 No.3989313 [Reply] [Original]

Hello /sci/ I come with a riddle, may you indulge in it?

You have a cup of coffee and a cup of cream.
You take a spoonful of cream and pour it in your coffee. Next, you take a spoonful of coffee and pour it in your cream.
Is there more coffee in the cream cup than cream in the coffee cup?

>> No.3989354

>>3989313
Nope, the ratio is the same.

>> No.3989357

>>3989313

I did it out because when I did it quickly the answer seemed wrong

Step 1, the givens:

Coffee=CO= 10/10ths CO
Cream=CR= 10/10ths CR

Step 2: cream in coffee

CO: 10/10ths CO, 1/10th CR
CR: 9/10ths CR

Step 3 reverse:

CO: 9.0909/10ths CO and .9090909/10ths CR
CR: 9.0909/10ths CR and .9090909/10ths CO

So the same

>> No.3989362

No, it'll be the other way around.

>> No.3989365

>>3989313
Harder riddles please.

>> No.3989367

>>3989357

as an addendum it depends on whether a spoonful is a percentage or a set value.

If set than the ratio is the same

If a percentage then there is more coffee in the cream

>> No.3989369

>>3989357
You have 11/10ths in that coffee cup.
You'd have to be taking 11/10ths of a tablespoon in order for that to work, but you're only taking 10/10th

>> No.3989379

>>3989369

I made a tablespoon equal to 1/10th of a cup for this riddle, as anyone that uses spoons know the value is set and unchanging and does not change reflecting the size of the glass.

Of course I had 11/10ths of liquid in my coffee cup, I just added 1/10th to it.

I don't even know what you're saying here please rephrase it

>> No.3989384

take 1g of coffee
put it in the cream
it diffuses evenly to make a 1/3 coffee-cream mix
take 1g of that
1/3 of 1/3 is 1/9 of the coffee that is given back
so 11/18 of the coffee is in the coffee cup

there must be more coffee in the coffee cup
1/2+1/9

>> No.3989387

No. You put cream in the coffee first, which taints the coffee. Then you take the tainted coffee and put it into cream. So you have more cream in your coffee than coffee in your cream.

>> No.3989396

>>3989384
did it backward

>> No.3989402

>>3989384

how many grams is the coffee cup starting at?

this is so hard to read its not even funny

>> No.3989417

you guys are almost all wrong

the trick of the riddle is to think that you are either giving back a percentage instead of a set value, or that you're getting less coffee into the cream cup so that it MUST be less.

The answer is that they are even

>> No.3989428

use the densities of coffee and cream, you are moving a VOLUME each time
you all lose
the game

>> No.3989433

is this more by volume or weight....

>> No.3989438

if the volumes are equal then they are equal quantities in each cup

>> No.3989445

The coffee cup contains:

Cup*Coffee+Spoon*Cream-\frac{Spoon^2}{Cup+Spoon}Cream-(1-\frac{Spoon^2}{Cup+Spoon})Coffee

The Cream Cup contains:

(Cup-Spoon)*Cream+\frac{Spoon^2}{Cup+Spoon}Cream+(1-\frac{Spoon^2}{Cup+Spoon})Coffee

Assuming that Cup > Spoon

>> No.3989450

"Milk has a density of between 1027 and 1037 kg/m3, at 20 degrees Celsius, depending on the type of milk. Water has a density of about 1000 kg/m3, at 20 degrees Celsius. Therefore, milk is more dense than water.

However, heavy whipping cream is less dense than water, due to the added milk fat. Heavy whipping cream is about 994 kg/m3."

monkey wrench in everyone's theories

>> No.3989471

cream is lighter than water and therefor has more volume by weight....

>> No.3989488

>>3989450

what I got from that is that coffee is more dense than cream.

So then the simple answer is that equal volumes of cream and coffee, there is more coffee.

so if equal volumes there is more coffee in the cream than vice versa

>> No.3989492

fluid dynamics tells us that liquids can be treated continuously
this means I can divide the coffee and the cream into an infinite number of pieces
thus no matter how much cream I pour into the coffee I never add any

QED

>> No.3989499

>>3989488
i think because of the fats you might be able to get a stronger surface tension bond in the cream than the coffee. i bet a spoon of cream could hold more than a spoon of coffee

>> No.3989511

>>3989499

maybe, but coffee has h bonds.

also heat plays a role if you want to go that in depth.

>> No.3989521

>>3989511
im no chem fag but i would have to guess that something colder would have better tension. also the coffee is going to be pretty hot... and the cream pretty cold... so maybe the cream is heavier anyway... the coffee only had a 6 parts out of 1000 head start....

>> No.3989573

>>3989492
what a douche

>> No.3989580

>>3989521
the coffee is no longer warm now, it probably was at the beginning of the riddle but you guys take too long to reach a consensus

>> No.3989602

>>3989580
you raise an interesting point. this is not some intellectual ideal of coffee and cream in our heads...first how long this is going to take us to solve and which will evaporate quicker? do we count bacterial mass as density in the cream or not? all important considerations....

>> No.3989626

the system's wavefunction collapses when you act as an outside observer

>> No.3989631

There is more cream in the coffee cup than coffee in the cream cup.

Its not that hard.

>> No.3989669

>>3989631
didnt you read the thread... its just not that simple....

>> No.3989658

>>3989626
at this point we also have to take into account the temperature and pressure changes that have occurred as since the coffee and cream were put out. temperature and pressure have changed because night has fallen ...

>> No.3989687

cup size = c
spoon size = s
assume s < c, significantly less
cream       coffee
c , 0           0 , c
     ==> [s,0]
c-s, 0 s , c

now what is the content of spoon next time?

[a,b] <==
a+b = s
a:b = s:c
a = b* s/c
b + b* s/c = s
b (1+s/c) = s
b = s/(1+s/c) = s/( (c+s)/c ) = c*s/(c+s)
a = b* s/c = s²/(s+c)

cream cup:
c-s + s²/(s+c) = ( (c-s)*(c+s) + s² ) / (c+s) = (c² - s² +s²)/(c+s) = c²/(c+s)
c*s/(c+s)

coffee cup:
s - s²/(c+s) = s*( 1 - s/(s+c) ) = s*( 1 - (1 - c/(s+c) ) ) = s*( c/(s+c) ) = c*s/(s+c)
c - c*s/(c+s) = c* (1 - c*s/(c+s) )

How about we suppose c = 1 (and 0<s<1)
we now have
  CREAM CUP      COFFEE CUP
c/(s+c) , s/(s+c)   s/(s+c) , 1-c*s/(s+c)
1/(s+1) , s/(s+1)   s/(s+1) , 1/(s+1)

> WELL THEY ARE EQUAL.
> :O

>> No.3989741

>>3989687
im just going to have to assume your reasoning is sound...

>> No.3989975

>>3989313

The volume in the coffee cup returns to the same amount (one tsp out, one tsp in). The coffee replaced by cream ends up in the cream cup. Clearly they are the same.

>> No.3990594

This problem doesn't warrant detailed analysis.
>You take a spoonful of cream and pour it in your coffee
>you take a spoonful of coffee and pour it in your cream
There is exactly one spoonful of coffee in the cream cup and one spoonful of cream in the coffee cup.

>> No.3990600

>>3990594
Then you don't understand the problem at all.

Remember, the first step was to dilute coffee with some cream. Then you took the diluted coffee/cream mixture and put it in the cream.


As for the riddle, I prefer my coffee black. Fuck off with your cream.

>> No.3990616

It's the same, Lewis.

>> No.3990623

>>3990600

I'd say this problem hinges on the ambiguous wording of the original sentence; Either solution is okay.

Reading it, he mentions that you take a spoonful, specifically, "of coffee". Not a spoonful "...Of diluted coffee from the coffee cup.". Depending on whether you assume he means that you simply take a spoonful from each or that he means he's actually purified his coffee spoon somehow until there's no cream left, then moved it over, you get different solutions.

tl;dr problem's stupid and easy either interpretation

>> No.3990634
File: 36 KB, 640x400, coffee_cream.jpg [View same] [iqdb] [saucenao] [google]
3990634

Given the spoonful is exactly the same for both scoops:

when the cream is poured into the coffee, a small fraction of cream will remain near the top of the cup of coffee. When you then proceed to take a spoonful of coffee, a small amount of cream will be taken back into the cup of cream. The transfer of coffee to the cream cup has a small % of cream, which varies. Take a look at my diagram. I show one case where most of the cream is returned to the cream cup, and another where very little cream is returned. In both "extreme" cases, the difference is the same. Taking a quick look at some middle ground, I noticed that the result was the same.

>> No.3990640

Think of it in terms of how much of each substance is being transferred each way.

From the cream to the coffee, 1 unit of cream is being transferred. From the coffee to the cream, 1 unit of coffee minus however much space the cream occupies. Even though we don't know how much that is, we know that there will be less then one unit of coffee in the cream.

So the cream has less coffee in it than the coffee has cream in it.