Coffee tea riddle

[disappoint]

From this thread:
http://forums.anandtech.com/showthread.php?t=2088452

Where they discussed the coffee tea riddle, but it was off topic from the OP so I decided to make a new thread.

so the riddle is:

Suppose you have 2 equally sized cups. One is full of coffee, one is full of tea. If a spoon full of coffee is added to the tea, the tea is mixed, then a spoon full of tea+coffee is added to the coffee, is there more tea in the coffee or is there more coffee in the tea?

Everyone seems to think they are equal in the end, I think not but maybe I'm wrong. I solved it like this:

cup 1: 100ml coffee cup2: 100ml tea
using 50ml spoon, 50ml coffee added to the tea then mixed
cup 1: 50ml coffee cup 2: 150ml of coffee tea mixture 50/50, so 75ml of coffee 75 ml of tea in cup 2
now, 50ml from cup 2 is put in cup 1. that is 25ml of coffee and 25ml of tea will go back into cup 1
cup 1: 75ml coffee, 25ml tea: cup 2 has 100ml of coffee tea mixture thats 50ml of coffee and 50 ml of tea.
there is more coffee in the tea than there is tea in the coffee.

Am I wrong? Where did I go wrong in the math?

 

[lokiju]

More coffee in the tea cup than tea in the coffee cup IMO.

 

[GodlessAstronomer]

More coffee in the tea cup than tea in the coffee cup IMO.

Seems obvious to me that this is the case, although I didn't put a lot of thought into it so I could be missing some subtlety.

 

[arkcom]

From this thread:
http://forums.anandtech.com/showthread.php?t=2088452

using 50ml spoon, 50ml coffee added to the tea then mixed
cup 1: 50ml coffee cup 2: 150ml of coffee tea mixture 50/50, so 75ml of coffee 75 ml of tea in cup 2

50ml of Coffee added to 100ml of tea magically becomes 75ml of coffee?

 

[disappoint]

50ml of Coffee added to 100ml of tea magically becomes 75ml of coffee?

I knew I screwed up somewhere, but I just didn't see it, thanks.

 

[arkcom]

I knew I screwed up somewhere, but I just didn't see it, thanks.

Think about this;
Each cup has 100ml of is respective drink.
You use a 100ml spoon to move coffee from cup 1 to cup 2 and stir.
Use the same 100ml spoon to move 100ml of that mixture back to cup 1.

 

[disappoint]

Think about this;
Each cup has 100ml of is respective drink.
You use a 100ml spoon to move coffee from cup 1 to cup 2 and stir.
Use the same 100ml spoon to move 100ml of that mixture back to cup 1.

Exactly the same. Boy the math sure is easier when you put it like that!
Thanks again.

 

[lord_emperor]

You have two awful tasting drinks.

 

[TuxDave]

Think about this;
Each cup has 100ml of is respective drink.
You use a 100ml spoon to move coffee from cup 1 to cup 2 and stir.
Use the same 100ml spoon to move 100ml of that mixture back to cup 1.

Well...

1) What if it's not a 100ml spoon?
2) What if the mixture isn't guaranteed to be mixed thoroughly?

(answer turns out the same but your simplification doesn't really answer the question well)

 

[biggestmuff]

WTF is there to even think about? More coffee in the tea cup than tea in the coffee cup.

 

[arkcom]

Well...

1) What if it's not a 100ml spoon?
2) What if the mixture isn't guaranteed to be mixed thoroughly?

(answer turns out the same but your simplification doesn't really answer the question well)

The question in its original form did not specify the size of the spoon. If the size of the spoon affects the answer, then it can't be answered.

 

[Fenixgoon]

maybe it's because it's late at night, but i'm getting equal fractions of coffee in tea and tea in coffee

100mL coffee, 100mL tea.

50mL coffee. 150mL coffee/tee (100mL tea, 50mL coffee)

coffee/tea is 2/3 tea, 1/3 coffee

50mL coffee + 50mL coffee/tea. 100mL coffee/tea

50mL coffee + 50*(1/3) = 66.66...mL coffee
50mL*(2/3) = 33.333....mL tea

100mL coffee/tea * 2/3 = 66.66mL tea
100mL coffee/tea * 1/3 = 33.33mL coffee

the fractions of coffee in tea and tea in coffee are equal.

or maybe i'm missing something here :hmm:

 

[drinkmorejava]

I got the same.

 

[MikeMike]

wouldn't a full cup, overflow when you add more liquid to it?

 

[Bill Brasky]

maybe it's because it's late at night, but i'm getting equal fractions of coffee in tea and tea in coffee

100mL coffee, 100mL tea.

50mL coffee. 150mL coffee/tee (100mL tea, 50mL coffee)

coffee/tea is 2/3 tea, 1/3 coffee

50mL coffee + 50mL coffee/tea. 100mL coffee/tea

50mL coffee + 50*(1/3) = 66.66...mL coffee
50mL*(2/3) = 33.333....mL tea

100mL coffee/tea * 2/3 = 66.66mL tea
100mL coffee/tea * 1/3 = 33.33mL coffee

the fractions of coffee in tea and tea in coffee are equal.

or maybe i'm missing something here :hmm:

I came to the same result. One cup is 2/3 coffee and the other is 2/3 tea. It made more sense to me when I realized the second transfer is carrying 16.6ml coffee and 33.3ml tea.

 

[Ken g6]

Or if you don't like thirds:

100ml tea / 100ml coffee / empty 25ml tea spoon
100ml tea / 75ml coffee / 25ml coffee in spoon
100ml tea + 25ml coffee / 75ml coffee / empty 25ml tea spoon
Now, taking a spoonful from the teacup gets: 100/125 = 4/5 tea, 25/125 = 1/5 coffee == 20ml tea, 5ml coffee, leaving:
80ml tea + 20ml coffee / 75ml coffee / 20ml tea + 5ml coffee in spoon.
80ml tea + 20ml coffee / 80ml coffee + 20ml tea / empty 25ml tea spoon

All nice round numbers; but I wouldn't have believed it if I hadn't worked it out myself!

 

[brblx]

obvious riddle is obvious. who the fuck doesn't know that 'an amount' is more than part of said amount? do you think the motherfucker in the riddle has a magical spoon that ONLY scoops a certain liquid from a homogeneous mixture?

 

[Bignate603]

obvious riddle is obvious. who the fuck doesn't know that 'an amount' is more than part of said amount? do you think the motherfucker in the riddle has a magical spoon that ONLY scoops a certain liquid from a homogeneous mixture?

I've got no idea what you're trying to say here...

 

[manlymatt83]

WTF is there to even think about? More coffee in the tea cup than tea in the coffee cup.

This. You originally moved pure coffee, but the second time you're moving mostly tea but SOME coffee.. Therefore, it's obvious that there's more coffee in the tea than tea in the coffee.

 

[Born2bwire]

This. You originally moved pure coffee, but the second time you're moving mostly tea but SOME coffee.. Therefore, it's obvious that there's more coffee in the tea than tea in the coffee.

They come out to be the same. What you forget is that when you move the coffee/tee mixture back into the coffee cup, there is LESS coffee in the cup that you are adding the mixture to than before. The fallacious thinking is in treating the amount of coffee in the cup as being constant.

Instead, what happens is that you add a little pure coffee into an amount of tea, and then add a coffee/tea mixture into a little less than amount of coffee.

 

[deadlyapp]

SO MANY FUCKING IDIOTS IN THIS THREAD

ilovecaps.

 

[SSSnail]

If you have FULL cup of coffee and a FULL cup of tea, and you don't drink it and start mixing the shits, I'm gonna smack you. And if you do, don't try to sue anybody for spilling this shit on yourselves because you were fuking around with the drinks instead of drinking them.

 

[TuxDave]

The question in its original form did not specify the size of the spoon. If the size of the spoon affects the answer, then it can't be answered.

Which is always a possibility if the riddle giver decides to be a dick

 

[deadlyapp]

Which is always a possibility if the riddle giver decides to be a dick

I don't think the size of the spoon affects it either. Even if the spoon is the size of the entire cup there is no change.

100mL cups. 100mL spoon.

Coffee cup has 0, tea cup has 100mL tea, 100mL coffee - 50/50
Take another spoonful and you have 100mL of a 50/50 mix so you still end up having perfectly equal differences, and in this case, the mixtures are the same as well.

 

[rhino56]

bah, i will stick to grape drink.