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Thread: Brain teaser#3

  1. #1
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    You have two glasses in front of you. One is full of orange juice and the other is equally full of lemonaide. You remove one spoonfull of lemonaide and put it into the orange juice, then one spoonfull of this mixture and put it back into the lemonaide.Is there more orange juice in the lemonaide or lemonaide in the orange juice?.

  2. #2
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    Let's see...suppose that one spoonfull equals 1% of the total contents of a given glass.

    1: When you put the spoonfull of lemonaide(L) in the orange(O) juice, you now have 100 parts O and 1 part L, so the orange juice is now 99.001% pure (100/101).

    2: Assuming that the two are first mixed thoroughly before one spoonful of that is taken out, you are now adding a mixture of 99.001% O and 0.999 % L to the lemonade glass. This means that you now have 99 parts L (remember, you took one part out) plus 0.999% of 1 part newly added that is also lemonade. So the lemonade glass now has 99.00999 parts L and .99001 part O. This means that the purity of the lemonade is: 99.00999/100 = 99.00999%

    So the lemonade glass is purer, and thus there is more lemonade in the glass of orange juice.

    If the percentage of a spoonful in relation to a glassfull is other than 1%, then the difference in purity varies proportionally.

  3. #3
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    Nov 2001
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    Incorrect

    Nice try though Guy.

  4. #4
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    <voiceover by Columbo>

    Y’ know, Guy’s explanation seems well-thought-out and everything, but there’s just one thing about it that bothers me. There is one thing that just doesn't add up. If the glasses end up equally full at the end of the exchange, then whatever amount of lemonade moved from one glass to the other must equal the amount of orange juice that moved in the opposite direction. That would mean they are of equal purity in the end – neither is purer!

    This one is easier to solve without a calculator. All those nines and zeros get jumbled up!

  5. #5
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    Apr 2001
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    Good Grief

    Marilyn Savant and Columbo just showed up. Actually I like both.

  6. #6
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    Carl sure has that simple but good point, the fact that both glasses are brought to the same volume means that their concentrations will be opposite but equal. So I must have muffed up somewhere!

  7. #7
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    Pekin, IL USA
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    Cool There is more lemonaide in the orange juice.

    The reason being is that you are adding one spoonfull of 100% pure lemonaide to the orange juice. A spoonfull of this mixture is less than 100% orange juice because of the percentage of lemonaide mixed with it.

  8. #8
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    Oct 2001
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    Insufficient information

    After the lemonade is added to the orange juice, is it stirred throughly? If so, you would then have one glass with X amount minus 1 teaspoon, then another glass with X amount plus one teaspoon. The glass with +1 contains a diluted mixture, and when a teaspoon is removed, the diluted misture contains both lemonade and orange juice. Added back to the lemonade, you have brought the two glasses back to X amount each. But, you just added lemonade and orange juice back to the lemonade, so the orange juice is more contaminated than the lemonade.

    But, if you just added the teaspoon of lemonade to the orange juice and did not stir vigorously, you then scooped mostly lemonade from the orange juice, leavely each glass about equally contaminated.

    This is the intuitive, serious answer, but I still suspect some joke is forthcoming. Something along the lines of, "The glass was COMPLETELY full, so the lemonade just ran over the side of the orange juice glass."
    Hindsight is NOT a plan!

  9. #9
    Join Date
    Nov 2001
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    131

    Bama, Information is sufficient

    Doesnt matter if stirred skimmed or whatever.Here is another way to view this. There is an absence of one substance,dont know axactly how much but we do know that another substance made up for the void. So the exact amount that is missing has to be the exact amount that was made up for or one glass would contain more liquid. Therefore each glass is equally contaminated.

  10. #10
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    I have to agree with Guy and Bama. The percentages in each spoonful were not equal as your last statement (Nate) would imply. Volume may be equal but concentration can not be in this scenario.

  11. #11
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    I'm thinking how to explain this to you, but, if there is even one molecule of lemonade in the mixture you put back in the lemonade glass, then you have more lemonade in the orange juice. Volume here is not the significant variable.
    Hindsight is NOT a plan!

  12. #12
    Join Date
    Oct 2001
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    Darn! I was wrong!

    While thinking of the solution, I realized I was wrong. Here is the way I thought of explaining it, and it comes out the same every time.
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~

    OK, let’s look at it this way:

    One glass is filled with 10,000 red beads, and one glass is filled with 10,000 white beads. We take 100 red beads and put them in the white beads. We then stir until there is a homogenous solution of red and white beads. We now have 9900 red beads in the first glass, and 10100 beads in the white glass. We now take 100 beads from the white glass, statistically containing 1 red bead. We now put these 100 beads back in the first glass. So, there is now 10,000 beads in each glass. 9,999 red and 1 white, and 9,999 white and 1 red.
    Hindsight is NOT a plan!

  13. #13
    Join Date
    Nov 2001
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    131

    Bama

    Excellent explanation. No matter what the combination of beads, as long as there is the same amount of beads in each container the colors are equal but opposite

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