Red Wine or White Wine
Two friends Johnny and Jade ordered a glass of wine each, Johnny red wine and Jade white.
Suddenly Johnny got an idea, he took a teaspoon of red wine and put it in the white wine glass, after mixing the wine he took a teaspoon of wine from that glass and mixed it back to the red wine glass. And he did it with so much precision (believe me !) that the quantity of both the glass were same after the transfer process.
Then ! he asks, "Can you tell me whether the red wine glass has more red wine than the white wine in the white wine glass or is it the other way round?".
Ofcourse you don't need wine glasses to solve this or do you?Labels: mathemagic, thinktank
posted by Rajesh Lal at
8:41 AM
40 Comments:
depends on how much each glass contained initially
depends on how much each glass contained initially
the red wine glass will have the same amount of red wine as the white wine glass has white wine and any left over red wine in the white wine glass will be the same as any white wine in the red wine glass
They have the same
Say he takes 5ml of red wine out and puts that in with the white wine, when he takes 5 ml out of the white wine glass there will be a small amount of red (say 1ml i know its not but just to simlify it).
100R in one glass 100W in the other
(95R)(100W 5R)
then take 5 out of that 4W 1R cause more white than red
(96R 4W) (96W 4R)
They will both have the same.
Say the cups have 2 teaspoons of wine. When you take 1 teaspoon of red and put it in the white, you know have 1 teaspoon of red in one glass, 1 teaspoon of red in the white glass and 2 teaspoons of white in the white glass. Take 1 teaspoon out of the white glass and put it in the red glass. Then you have 1.5 teaspoons of red in the red glass and .5 teaspoons of white in the glass and 1.5 teaspoons of white in the white glass and .5 teaspoons of red in the white glass.
Say you have 3 teaspoons in each glass. When you take 1 teaspoon out of the red glass and put it in the white glass you and vice versa you end up with 2.25 teaspoons of red in red glass and .75 white in red glass and 2.25 white in white glass and .75 red in white glass.
red glass white glass
red white red white
3 0 0 3
2 0 1 2
2.25 .75 .75 2.25
It doesn't matter how much is in the wine glasses.
Thank you
It doesn't matter how much is in each glass, and they are not the same in the end. The first teaspoon (red glass to white glass) poured is 100% red wine. The second teaspoon (white glass to red glass) would be mostly white with a small percentage of red from the initial transfer. No matter how many times this is repeated the "white" glass will always be less pure than the red. The key is that the processes are sequential rather than simultaneous, and include a mixing of the wine between them.
This is very simple and obvious! It does matter how much wine is in both of the glasses. If they only have a teaspoon of wine each then you have a glass that contains one tsp of red wine and a glass that contains one tsp of white wine... and you take the rw and put it in the ww glass that means that the ww glass is now a 50/50 mixture, once you put the one tsp back in the "empty" rw glass both glasses now have the same amount of red and white wine.
depending on how much wine is in each glass... one tsp would be a certain percentage of the glass. Sequentially mixing the wines would reduce the percentage. say both glasses were full... then the rw glass would still have more rw.
For the comment above, assuming a consistent mixture of red and white above, if you actually calculate the percentages (however small they might be considering the size of the wine glass) you would see that it doesn't matter the amount.
Of course the red one has less than.
because it be taken a whole 1 tsp but get back only half tsp of ww.
the red wine glass has more red wine than the white wine in the white wine glass do to it being in series just by a small amount
Here's the simple (easily divisible) math of this:
Each glass contains 60 parts of their respective fluids
WG=60w;RG=60r
Take 12 parts from the red glass and dump it into the white glass, where the mixture presumably achieves a uniform distribution of 5w:1r
WG=60w,12r;RG=48r
Now take 12 parts from the white glass (10w:2r) and dump it into the red glass
WG=50w,10r;RG=50r,10w
And behold! Inverse proportions without those vexing decimals (vexidecimal?)
The red wine glass would have less white wine than the white wine glass has red wine. When red wine is transfered to the white wine glass and mixed in, you have part red and part white wine in the glass. Then, you take a spoonful of the mixture, red + white, and put it back into the red wine glass. Consequently, some of the red wine is going back to the red wine glass. Therefore, the red wine glass will have more red wine and less white wine becasue it is a mixture that is coming back and a pure red that is going over.
There is more red wine in the red wine glass besause he had already mixed the red wine into the white wine glass so when he took the white wine from from his glass, there was red wine in it.
Thanks for reading!!!!
There is more red wine then white wine because the white wine that went in to red wine already had some white wine
The red wine glass.
Redwine glasses are larger than white wine glasses,
therefore they'd have more liquid. :)
This post has been removed by the author.
Since the white wine was diluted with red wine initially, any amount of white wine transferred to the red wine glass would contain trace amounts of red wine. The glass of red wine would never be diluted with the same amount of white wine as the white wine is diluted with red.
So no, even though both glasses include the same measure of wine, they would not contain equal mixtures.
No math involved in this one--simply logic.
it already states that they had the same after transferring. so obviously, neither
Lets R stand for the red wine glass and W stand for the white wine glass
the teaspoon of red wine has 100% red wine called T and the next teaspoon is X
when mixed with the white wine the next teaspoon will have a larger portion of white wine than the red wine, lets say 75% of the teaspoon is white wine and 25% is red wine.
when added to R it would be R-1/4T.
the white wine would have W - 3/4X
in conclusion... R-1/4T> W-3/4X meaning that there is more red wine in the red wine glass that white wine in the white wine glass
The red wine glass has more red wine.
Why? Think logically.
Lets say both the glasses have an equal amount of wine, 100ml. Let in each teasppon, there is 10ml of wine. So, Johnny took 10ml of red wine and put MIXED it in the glass of white wine. So. the glass with red wine now has 90ml of red wine while the other glass has 100ml of white wine+10ml of red wine. Then, Johnny takes a teaspoon of wine from the white wine glass and MIXED it in the red wine glass. Note that Johnny did not take 10ml of white wine but a mixture of white and red wine. If Johnny only did the transfer just once, the red wine glass would have more red wine. Note that a transfer of 10ml of wine from the white wine glass into the red wine glass would again make the quantity of wine in the red wine glass 100ml. So, it is not wrong so assume that he did it once. If Johnny did it many times, let's say 2 to 5 times, I would say that the red wine glass has more red wine still. If Johnny did it many many many times till he got old or till all of the wine evaporated, I would say that i have no idea.
LOL
they will both look red but the white wine will not be as sharp
there is more in the white wine glass because the first spoonful was only red wine put into white wine so the spoonfuls put into the red wine glass was always mixed with white wine. So one full spoonful of red wine was put into the white wine glass followed by mixtures of both till finished, but the red wine glass was always filled with a mixture of red and white wine.
if each glass has one teaspoon each then they are the same, because he put all the red wine which was one teaspoon into one teaspoon of white wine making it 2 teaspoons of 1/2 red and 1/2 white, 1 teaspoon of red, one of white. then he put 1 teaspoon of the 1/2 red and 1/2 white into the red glass making half the red glass white and the white glass red.
say each glass has 20cl (6/6) of wine in it, and a tsp holds 10 (3/6) cl of liquid. when 10 (3/6) cl is transferred from red wine to the white wine, the white wine would be 2 parts (6/6) white and 1 part (3/6) red. now take 10 (1/3 total liquid in white glass) cl from the white wine glass, that means u have taken 2/6 of the initial white wine leaving 4/6 and taken 1/6 of the red leaving 2/6, and put it back into the red wine glass. the total liquid in each glass is 4/6 red + 2/6 white and 4/6 white and 2/6 red.
this is going by the wine being equally mixed and you taking out equal proportions.
even if you took out more red from the white wine glass you are leaving the same amount of red as you are taking white. so the answer is they would end up being the same.
the only problem i have is, jonny just ruined jade's wine without asking her. and i dont think that is right.
ethan the red wine would look red, the white would look rose, but still both would contain opposite ammounts of each wine.
the amount of whit wine taken out of the mixture would be equal to that of the red wine left in the mixture so both would end out opposite measures
Red wine has more purity than the white wine. If you take one teaspoon of red wine out of the red wine glass and put it into the white wine glass. The only way to reach equality again is to take one teaspoon of straight white wine and put into the red wine glass. Every teaspoon of white wine will be contaminated with red wine. If we were dealing with oil and water...maybe there could be a difference.
After having a few hours sleep, I have to change my answer to 50/50.
ok..ok...now i'm thinking on this too hard.
Let me simplify it a bit. lets say that each glass has 3 teaspoons in it.
3tp red
3tp white
remove one tp of red and put it in white
2tp red
3tp white 1tp red
now the teaspoon from the white glass is actually not a 50/50 mixture, but a 75/25 mixture.
so by adding the white wine teaspoon back into the red you get
(2.25 red .75tp white) red glass
(2.75 white .25tp red) white glass
So after 3 guesses, my final answer is the white wine has more of the original content.
brian, look at the total of wine uve got
2.25 red + .25 red = 2.5 red
2.75 white + .75 white = 3.5 white
where did this extra white come from, and where did the red go?
| | | | wines poured
|RRR| |WWW| Red = 9 red
|RRR| |WWW| 0 white
|RRR| |WWW| White = 0 red
|___| |___| 9 white
| |
| |
__|__ __|__
|WWW| | | tsp moved
|RRR| | | red = 9 red
|RRR| |WWW| 3 white
|RRR| |WWW| white = o red
|___| |___| 6 white
| |
| |
__|__ __|__
|WRR| | | stirred
|RRW| | | red = 9 red
|RRR| |WWW| 3 white
|RWR| |WWW| white = 0 red
|___| |___| 6 white
| |
| |
__|__ __|__
| | | | tsp moved
|RRW| |WRR| red = 7 red
|RRR| |WWW| 2 white
|RWR| |WWW| white = 2 red
|___| |___| 7 red
| |
| |
__|__ __|__
ok ok so i used wine glasses
it helps lay it out for you
hey the glasses didnt stay :(
thats not good
listen to the question people. they cant be equal, its one or the other. And Only the red wine lost a "FULL" teaspoon! So it has to be more in the white wine.
cwell out!
let me explain a little more. The red wine was the first to be taken out right?. It wasn't mixed with anything, it was just a full teaspoon red wine. Thats what i meant by "it lost a full teaspoon". Now the white wine has been mixed......so you cant get a full teaspoon of just white wine right?. So theres more white wine then red wine.
cwell out.
White Wine will be more
one full teaspoon of red wine was taken from the red wine glass.
one teaspoon of white wine was taken from the white wine glass.
whatever amount of white wine was taken out of the white wine, was equal to that of the red wine wine left in the white wine glass
-------rrr--->rww
www--->www--->www--->www
www--->www--->wwr--->wwr
www--->www--->wrw--->wrw
rrr--->------>------>rww
rrr--->rrr--->rrr--->rrr
rrr--->rrr--->rrr--->rrr
there were 2 parts white wine in the teaspoon, and 2 parts red in the wine. the only way the amount could be different is if he repeated this again.
i love how very few of you can see shapes and spaces very very well.
in fact it doesnt matter how many times it is repeated, you will still get the same answer they are both equal in opposite quantities
www---rrr
www---rrr
www---rrr
rrr------
www------
www---rrr
www---rrr
rww------
wrw------
www---rrr
wwr---rrr
wrw---rww
www---rrr
wwr---rrr
wrw---rrr
www---wrr
wwr---rrw
rrr------
wrw------
www---wrr
wwr---rrw
wwr------
rwr------
wrw---wrr
rww---rrw
rwr---wwr
wrw---wrr
rww---rrw
rrr---www
rww---wrr
www---rrr
thats 2 teaspoons done and theyre still the same, you will always take the same amount of white as you have left red......or summin like that.....but still it will always be the same, untill he uses a larger spoon
wow, this one had me fooled at first. It makes you really want to thing there's more red wine in the red wine glass.
If, after no matter how many teaspoon-transfers, both glasses are equally full and the white wine glass contains x parts of red wine, then those x red wine parts must be missing in the red wine glass. But both glasses are precisely as full as they were before the transfers, so the liquid filling the red wine glass must be white wine, exactly x parts. Both glasses are equilly diluted.
ANSWER
-------------------------
both glass have same wine
Details
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Best and creative explaination by mo
"If, after no matter how many teaspoon-transfers, both glasses are equally full and the white wine glass contains x parts of red wine, then those x red wine parts must be missing in the red wine glass. But both glasses are precisely as full as they were before the transfers, so the liquid filling the red wine glass must be white wine, exactly x parts. Both glasses are equilly diluted."
GOT RIGHT
-------------------------
Zack Redstar, jonathan, Seth and GREAT thinking by mo
the question is misleading...
"Can you tell me whether the red wine glass has more red wine than the white wine in the white wine glass or is it the other way round?".
therefore, the option of being equal was not available.
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