Coffee Cup Tea Cup logic

[TakenItSeriously]

You have a coffee cup holding exactly 1 cup of coffee and a tea cup holding exactly 1 cup of tea.

 

Using a standard sized teaspoon, you transfer one teaspoon of coffee and mix it in with the tea. You then transfer a teaspoon of that mixture back into the coffee cup.

 

Question:

A) Is there more coffee in the tea cup

B) Is there more tea in the coffee cup

C) Or are the amounts the same?.

 

Justify your answer.

[Phi for All]

You have a coffee cup holding exactly 1 cup of coffee and a tea cup holding exactly 1 cup of tea.

 

Please clarify, does "a tea cup" hold "exactly 1 cup" of liquid (in this case tea), or does it hold more?

 

It will make a difference if the tea cup holds "exactly" one cup, since you'll be displacing tea out of the cup when you put an extra spoon of coffee in the tea.

[imatfaal]

let cup be w and spoon z. x is tea and y is coffee. you end up with

 

(wx+zy)*(w/(w+z) in the cup that you added to and then took from

 

wy-zy+(wx+zy)*(z/(w+z)) in the cup that you took from and then added to

 

both simplify to similar expressions

 

(w(wy+zx))/(w+z)

 

and

 

(w (wx+zy))/(w+z)

 

You will notice that they are the same apart from the x and y are switched ie you end up with the same ratio in each cup - but obviously one is ratio of coffee to tea and the other tea to coffee

[TakenItSeriously]

Please clarify, does "a tea cup" hold "exactly 1 cup" of liquid (in this case tea), or does it hold more?

 

It will make a difference if the tea cup holds "exactly" one cup, since you'll be displacing tea out of the cup when you put an extra spoon of coffee in the tea.

Both cups have room for more liquid, and their initial volumes were equal.

[imatfaal]

Intuitively - you end up with Spilt tea and Phi calling you names for messing up his carpet.

 

Heuristically - it must be the same ratio as you end up with the same amount in each cup. If you both started and ended with a cup of tea and a cup of coffee (however distributed) you must end with a cup of tea and a cup of coffee; and as each cup has same volume in at end the yo must have as much coffee in the tea cup as tea in the coffee cup

[TakenItSeriously]

let cup be w and spoon z. x is tea and y is coffee. you end up with

 

(wx+zy)*(w/(w+z) in the cup that you added to and then took from

 

wy-zy+(wx+zy)*(z/(w+z)) in the cup that you took from and then added to

 

both simplify to similar expressions

 

(w(wy+zx))/(w+z)

 

and

 

(w (wx+zy))/(w+z)

 

You will notice that they are the same apart from the x and y are switched ie you end up with the same ratio in each cup - but obviously one is ratio of coffee to tea and the other tea to coffee

Correct!

 

Excellent analysis, recognizing symmetry is the key.

Intuitively - you end up with Spilt tea and Phi calling you names for messing up his carpet.

 

Heuristically - it must be the same ratio as you end up with the same amount in each cup. If you both started and ended with a cup of tea and a cup of coffee (however distributed) you must end with a cup of tea and a cup of coffee; and as each cup has same volume in at end the yo must have as much coffee in the tea cup as tea in the coffee cup

Also correct, and very quick at finding the logical shortcut. Nice job.

 

In Layperson: since both volumes started and ended up being a cup, what was missing from one, had to be replaced by the same amount of the other.

Correct!

Excellent analysis, recognizing symmetry is the key.

 

Also correct, and very quick at finding the logical shortcut. Nice job.

In Layperson: since both volumes started and ended up being a cup, what was missing from one, had to be replaced by the same amount of the other.

I'll just skip ahead to a tougher problem, have you head the riddle about finding the odd ballbearing from a set of 12 ballbearings?

[imatfaal]

there is a number of huge threads on coin/ball bearing weighing; including some neat proofs and algorithms.

 

here is one of my favourites if you like this sort of thing - please no open spoilers here. And apologies I should have put my answers in spoiler tags

 

 

 

http://www.xkcd.com/blue_eyes.html

[TakenItSeriously]

there is a number of huge threads on coin/ball bearing weighing; including some neat proofs and algorithms.

 

here is one of my favourites if you like this sort of thing - please no open spoilers here. And apologies I should have put my answers in spoiler tags

 

 

 

http://www.xkcd.com/blue_eyes.html

When you say "please no opens spoilers here" are you referring to this this thread or the link you posted.

 

Actually, given the title of the problem, I have my doubts as to my chances for solving it though it's a rare experience for me so I wouldnt mind continuing with some questions.

 

Is the statement that everyone can see everyone else 100% of the time. Should that be taken literally? I believe I may have a solution, if such is not the case.

[michel123456]

You have a coffee cup holding exactly 1 cup of coffee and a tea cup holding exactly 1 cup of tea.

 

Using a standard sized teaspoon, you transfer one teaspoon of coffee and mix it in with the tea. You then transfer a teaspoon of that mixture back into the coffee cup.

 

Question:

A) Is there more coffee in the tea cup

B) Is there more tea in the coffee cup

C) Or are the amounts the same?.

 

Justify your answer.

Ok

Both cups were filled exactly to the edge, is that it? Call it Vc and Vt (Volume of coffee & Volume of tea)

In this case, when you put the tea spoon in the first coffee cup a volume of coffee is splitted out, it corresponds to the volume of the tea spoon itself (called Vts1), not the contenance of the tea spoon (called Cts)

Step1. When you take out the tea spoon, the volume inside the coffee cup is less: you have Vc-Vts1-Cts=A

 

Step2.Then you put the coffee (Cts) in the tea cup, you can do that by pouring without putting the tea spoon into the liquid. Some liquid is spiltted out (because the the cup was already full, and the resulting volume remains the same = Vt

 

Step3. You put the tea spoon entirely into the tea cup and mix the liquid. Some liquid is spilled out again because the tea spoon has a volume Vts2 (here we ignore the difference in volumes because the tea spoon is immersed fully and consider Vts1 =Vts2).

 

Step4.You take the tea spoon out with the liquid, resulting in a cup having Vt-Vts1-Cts=B

 

Step 5. You pour the liquid in the first cup and you get A+Cts = Vc-Vts1

 

Thus you have Vc-Vts1 and Vt-Vts1-Cts , for Vc=Vt it means the first cup has more than the other

Edited July 9, 2016 by michel123456

[TakenItSeriously]

Ok

Both cups were filled exactly to the edge, is that it? Call it Vc and Vt (Volume of coffee & Volume of tea)

In this case, when you put the tea spoon in the first coffee cup a volume of coffee is splitted out, it corresponds to the volume of the tea spoon itself (called Vts1), not the contenance of the tea spoon (called Cts)

Step1. When you take out the tea spoon, the volume inside the coffee cup is less: you have Vc-Vts1-Cts=A

 

Step2.Then you put the coffee (Cts) in the tea cup, you can do that by pouring without putting the tea spoon into the liquid. Some liquid is spiltted out (because the the cup was already full, and the resulting volume remains the same = Vt

 

Step3. You put the tea spoon entirely into the tea cup and mix the liquid. Some liquid is spilled out again because the tea spoon has a volume Vts2 (here we ignore the difference in volumes because the tea spoon is immersed fully and consider Vts1 =Vts2).

 

Step4.You take the tea spoon out with the liquid, resulting in a cup having Vt-Vts1-Cts=B

 

Step 5. You pour the liquid in the first cup and you get A+Cts = Vc-Vts1

 

Thus you have Vc-Vts1 and Vt-Vts1-Cts , for Vc=Vt it means the first cup has more than the other

The assumption that the useage of coffee cup and tea cup indicates that they each hold exactly one cup which wasnt the intended meaning. Sometimes a cigar is just a cigar.

 

Unfortunately I can't edit the op to make it more clear. Which is why I hate word play riddles. They make logic riddles so difficult to write

Edited July 9, 2016 by TakenItSeriously

[imatfaal]

When you say "please no opens spoilers here" are you referring to this this thread or the link you posted.

 

Actually, given the title of the problem, I have my doubts as to my chances for solving it though it's a rare experience for me so I wouldnt mind continuing with some questions.

 

Is the statement that everyone can see everyone else 100% of the time. Should that be taken literally? I believe I may have a solution, if such is not the case.

 

 

I think Randall's explanation is good - yes literal interpretation; everyone can see everyone else all the time.

 

On the spoilers - it is always better to use spoilers so that people can read without the problem be ruined for them; this was my fault entirely -Sorry

 

Spoiler tags work like this

 

[spolier] text to be hidden [/spolier]

 

which if you spell spoiler correctly gives this

 

 

text to be hidden

 

[TakenItSeriously]

I think Randall's explanation is good - yes literal interpretation; everyone can see everyone else all the time.

 

On the spoilers - it is always better to use spoilers so that people can read without the problem be ruined for them; this was my fault entirely -Sorry

 

Spoiler tags work like this

 

[spolier] text to be hidden [/spolier]

 

which if you spell spoiler correctly gives this

 

 

text to be hidden

 

 

I got the spoiler tags, thanks. I added them to my KB shortcuts.

 

Re the island, I have a possible solution.

 

So the idea that everyone can see everyone else at all times invalidates my first guess:

The person who left the island was able to deduce his own eye color based upon the fact that no blue eyed person was in the vicinity when the Guru stated that she could see a blue eyed person.

 

My second guess:

If it's correct, I don't think I can take credit because I'm beginning to think Ive read the riddle before.

 

The ferryboat captain presumably leaves at some time after midnight, since he arrives every night at midnight.

 

 

 

BTW:

Here is one sentance that comes across as confusing, in case you wanted to let your friend know.

No one knows the color of their eyes

Which I took to mean:

No one on that island knows the color of their own eyes.

[michel123456]

The assumption that the useage of coffee cup and tea cup indicates that they each hold exactly one cup which wasnt the intended meaning. Sometimes a cigar is just a cigar.

 

Unfortunately I can't edit the op to make it more clear. Which is why I hate word play riddles. They make logic riddles so difficult to write

The statement was

 

You have a coffee cup holding exactly 1 cup of coffee and a tea cup holding exactly 1 cup of tea.

 

Using a standard sized teaspoon, you transfer one teaspoon of coffee and mix it in with the tea. You then transfer a teaspoon of that mixture back into the coffee cup.

 

Question:

A) Is there more coffee in the tea cup

B) Is there more tea in the coffee cup

C) Or are the amounts the same?.

 

Justify your answer.

---------------------------------------------------------------------

Excellent analysis, recognizing symmetry is the key.

This is ridiculous. The symmetry looks so obvious, you don't have to "recognize" it. If you accept symmetry, the answer is also "obvious". And wrong IMHO.

 

I believe the point is, or should be, that in order to make a movement (take coffee from one side and put it on the other side) you need somewhere empty space. IOW you cannot continuously have both cups full of liquid AND make the move. Which has the result that after the move, this tiny empty space remains*.

Now, if the empty space already exists by thinking that the cups are not filled up, then the problem is stupid.

 

*like a sliding puzzle. https://en.wikipedia.org/wiki/Sliding_puzzle

Edited July 9, 2016 by michel123456

[John Cuthber]

For the sake of discussion, can we assume that a "cupful" is a defined volume and the drinks are served in oversize cups (to avoid spillage)?

[TakenItSeriously]

For the sake of discussion, can we assume that a "cupful" is a defined volume and the drinks are served in oversize cups (to avoid spillage)?

Yes please,

 

I did try to post it a couple times, but apparently it didnt take and I cant modify the OP.