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Two tumblers, I and II, contain equal volumes of pure liquids A and B respectively.
A spoonful of liquid A is taken from tumbler I and transferred to tumbler II.
The contents of tumbler II are stirred.
A precisely-equal spoonful of the contents of tumbler II is now transferred to tumbler I.
At the end of this operation, which of the liquids is the less contaminated?
(I’ll explain a few days from now why I selected this question.)
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I worked it out. I'll give a bit of time for people to vote before I explain it publicly.
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Well, I voted, but I feel like I'm missing something here. I seem to remember hearing about this before, but the way the math is working out when I do it is not what I seem to remember from before.
At any rate, I voted the way my math works out, so when we're all done here I'll find out what I'm forgetting!
Established Member
Heh... that's kinda neat. when I did it in my head, it could have gone either way, but on paper it was pretty obvious (which probably means my answer was wrong...) :-?
Honored Member
The correct answer is to choose the third door.
Established Member
My mind is going...I can feel it...I can feel it....
[Desperatly gathering the rement of a once great intelligence]
Old, half forgotten memories of a bology experiment (which probably had nothing to do with the question
Now just the wait to see the right answer
Order of Kilopi
I think it may be possible that the problem is not well specified. It may be necessary to know how much liquid was in each container to start with.
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Come on now!
The true answer is...
There is no spoon!
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We are told that there are equal volumes of each liquid in each tumbler.Originally Posted by Donnie B.
Honored Member
And the answer behind door three is: equal.
If you don't treat it as a Marilyn Vos Savant Parade problem but just as concentration problem in chemistry, it's easier.
Now, how much wood could a woodchuck chuck...
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Well, since Mike has revealed it, I'll post what I sent to mutineer.
Honored Member
Glom&mutineer:
I didn't think I revealed it. Well, I didn't mean to reveal it.
How was I supposed to know there were so many chemists out there?
Oh, well... at least learn something from Feynman. Wasn't he the one who said if you don't understand the problem, recast it in a form you can understand?
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ops:
Honored Member
No
Besides, when I'm angry my rants tend to go on a lot longer. And the Vos Savant was extremely clever, don't you think? :wink:
What I will say is that I could not solve the problem until I recast it as a concentration problem. The old 'bag of tools' thing.
Established Member
Sorry, Donnie. I guess it's too late now. I forgot to mention that the operation was carried out by a right-handed male, on a weekday, in the northern hemisphere. Also, that no overflow occurs, and that you are not allowed to use math to get the answer.
Don't worry mike! So far as I'm concerned, you didn't reveal nuthin!
Sorry, Glom, your answer is wrong. It's the first sentence that's wrong.
The correct answer can be explained without math in a single sentence!
Anyone want to take up the challenge?
Appreciated your answer, parejkoj! You really did get the answer, I think - i.e. the answer to why I found it a nice question.
I'll be back to say more.
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Not a chemist....
Start with 1000 ml in each tumbler. Take 500ml of A and add to B. This makes:
Tumbler 1: 500ml of liquid A. Tumbler 2: 1000ml of liquid B and 500 ml of liquid A. Stir. I have to assume a good mixture, because I don't know how to do it otherwise. Now, take 500ml of solution AB and add back to Tumbler 1. I think it ends of like this:
The 500ml of AB transfered should be 1/3 A, or approx 167 ml, and 2/3 B or approx 333 ml. That gives a total of 667 ml A and 333 ml B in Tumbler 1.
That leaves 333 ml of A in tumbler 2. So, they are equally contaminated...
Darn, I shoulda writen it out first... I worked it out in my head and thought B would be more contaminated
Established Member
Um guys, I might be missing something, but in the setup of the problem it never says that either of the liquids are contaminated......could be just me though, I'm no chemist
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Intuitively, I think tumbler 1 is less contaminated since you are putting a tiny fraction of it's original liquid back in it.
Honored Member
Oh. Of course. What an idiot (sel-referential).
If you pour all of A into B, mix well, then pour half back, the concentrations will be equal.
(I think Martin Gardner appeared to me in a dream...)
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cyswxman, that's what I thought too, but I worked it out (see above), and I think that they are equally contaminated.
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Well then, what is it?
Established Member
I got it wrong...
Could the real answer be, 'Driving Miss Daisy?'
Established Member
Ah, you're an impatient fellow, Glom!
Apologies if I sounded impolite when I said your answer was wrong earlier - but really the sentence "I simplified things slightly" was not quite right! Using math is not the simple route.
I promise you that the correct solution can be explained in about thirty words of simple logic. (You might need to use a semicolon or two to keep it down to a single sentence.) Thing is, you need to come at the thing from a new direction - and suddenly it's a cinch! The correct solution is just unbelievably obvious.
I won't keep you waiting forever!
Order of Kilopi
mutineer,
Glom's final answer was that "[t]he contamination is equal."
Are you saying that is wrong, or just that his solution wasn't really "simplified" because there's a simpler way to get it?
Established Member
The final answer was right. If you tackle to the IQ Question with math, you get the right answer (unless your arithmetic is at fault). I was hoping that people would treat it as a logic problem. BABBers go for a math approach far more readily than a "normal" population. It is entirely sensible and practical to use math - but less of a test of reasoning and mental agility (i.e. less of a test of IQ).
But Glom did not "simplify things slightly". It was that first sentence that I took objection to. Compared to the simple logical solution which I will finally present**, he "complicated things enormously".
**But I'd love someone else to come up with the perfect simple solution.
Established Member
I'm sticking with my assertion that it was never stated that neither solution was said to be contaminated, therefore both have equal, and zero, contamination.
Order of Kilopi
How about this. At the end of the experiment, both tumblers have the same amount of liquid they started with, so and missing A liquid in tumbler one is replaced by the same amount of B liquid. Therefore, they will have the same amount of contamination...
Established Member
That's about it, Musashi!
Here is my own general explanation of the IQ Question:
-----------------------------------
There are two solutions to the IQ Question, each of which requires only a moment’s thought – but which produce contradictory answers.
(1) The first spoonful consists entirely of liquid A, but the second consists of a mixture – so the second produces less contamination. Therefore liquid A is the less contaminated.
(2) The two transfers leave equal volumes of liquid in each tumbler. The volumes of liquids A and B are equal. Thus, the amounts of contaminant in each tumbler must also be equal.
If both solutions occur to one, then one must look for an error in one of them. After further thought, one realises that (1) overlooks the fact that the second spoonful reduces the amount of contaminant in tumbler B. But (2) is logically flawless, and produces the correct answer.
I'll be back to say a few words more about why I selected the question.
Honored Member
Oh, poopy. (MST3K)It is entirely sensible and practical to use math - but less of a test of reasoning and mental agility (i.e. less of a test of IQ).
Established Member
OK...
Assume both tumblers contain 20 ml each. 1 spoon = 5 ml
Take 5 ml of A and mix with 20 ml of B. Mix becomes 25 ml, 4 parts B to 1 part A.
Take 5 ml of mix, which is 4 ml B and 1 ml A. Mix with 15 ml of remaining A.
Tumbler 'A' now has 16 ml A + 4 ml B.
Tumbler 'B' now has 16 ml B + 4 ml A.
Hence both have the same amount of cross contamination, and my origional assumption was incorrect. Can I have a re count?
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