Erin:
Suppose you have 1 tsp of coffee in mug1 and 1 tsp of milk in mug2.
You put all the milk (1 tsp) into the coffee. Now there's nothing in
mug2. Mug1 has 2 tsp of liquid that's 50-50 coffee/milk. When it's mixed,
and you take a tsp of this, it will be 50-50 also (1/2 tsp coffee, 1/2 tsp
milk). When you put this back into mug2, both mugs will be 50-50.
Andrea's proof is very nice.
Glenn
Erin Noonan <enoonan@kent.edu> wrote:
>>Erin, if I understand your question, yes, it is a given that regardless of
>>whether the liquids are mixed or not, that the teaspoon is a constant
>>volume. There is no 50-50 mixture involved: in the first move, a teaspoon
>>of milk is put into the coffee mug, which is then stirred throroughly, and a
>>teaspoon of the mixed liquid is then taken from the coffee mug and put into
>>the milk mug....
>>
>>Lawry
>>
>
>No I understand what you are saying but everytime I imagine it
>the teaspoon of milk + coffee mixture going to mug 2 seems like it has to have
>less then the tsp of undiluted milk going to mug1.
>I just can't picture how everyone gets them to be even.
>So I was asking more with Glenn's adding 1 tsp of coffee with
>1 tsp of milk does that always equal 2 tsps liquid. Or does
>the process of "dissolving" affect overall volume.
>I just can't see how one tsp of undiluted milk put in mug 1 will become
>equal to the 1 tsp diluted coffee put in mug 2.
>That tsp of diluted coffee has to have some milk taking up the 1 tsp volume.
>uuuuuuuuuuuuggggggggggggggggggggg
>Serious block on this puzzle,
>
>erin
>
>
> (>>
>>> hi glenn,
>>> Okay I can not get this one through my head yet. I get lost
>>> reading Andrea's solution. This one I can imagine better but
>>> this one I am just wondering is taking half of that 50-50 mixture
>>> definitely 1 tsp? That is when 1 tsp of coffee and 1 tsp of milk
>>> are mixed until milk dissolves is it always 2 tsp?
>>>
>>> erin
>>>
>>> >I agree with Joćo's conclusion. After the two pourings, the amount of
>>> >coffee in mug1 is the same as the amount of milk in mug2. It follows
>>> >also that the amount of milk in mug1 is the same as the amount of coffee
>>> >in mug2.
>>>
>>> >While not a proof, the easiest way to see this is to try simple cases.
>>> >Suppose both mugs have 1 tsp of liquid. When you pour all the milk from
>>> >mug2 to mug1, mug1 now has a 50-50 mixture. When half of that is returned
>>> >to mug2, both mugs have a 50-50 mixture.
>>>
>>>
>>>
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>>
>>
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>
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