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A spoon of wine is poured from a barrel of wine into a (not full) glass of tea. After that, the same spoon of the (inhomogeneous) mixture from the glass is taken back into the barrel. Now both in the barrel and in the glass there is a certain volume of the foreign liquid (wine in the glass and tea in the barrel). In which is the volume of the foreign liquid greater: in the glass or in the barrel?
(Taken from: https://www.imaginary.org/sites/default/files/taskbook_arnold_en_0.pdf
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You just ruined a perfectly good barrel of wine.
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Mathematics checks out. but I wonder if someone can explain this conceptually.
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I mean... It all depends..
Is it a physics puzzle or a math puzzle?
I'll take your word for it. But I'm trying to figure out how it works.
If it's a math puzzle am I right in saying that the size of the two vessels doesn't matter and that the information about the cup and the barrel is just a red herring?
Some quantity of wine, S, is introduced to the cup. Then some quantity of wine, x, is removed from the cup along with some tea. So the quantity of wine in the cup is S-x.
As for the barrel. There is x wine in the spoon. So there must be S-x tea in the spoon. You dump that all in the barrel and both have S-x foreign liquid.
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the size of the cup and barrel don't matter
But I suppose you must assume that you can still measure up a spoonful of each.
Also that the wine mixes completely with tea, which is in the real world not necessarily the case.
To me it is mostly a math puzzle in understanding how mixed liquids work. reminds me of those chemistry class volumetric calculations work. I remember having a part of a semester being thaught that when I was in high school, I think.>>1090444
That's at least already a simplification on what I was thinking.
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Talking about math, I should probably spend some time thinking about the equilateral triangle one:
Equilateral triangles are constructed externally on
sides AB, BC and CA of a triangle ABC. Prove that
their centres (∗) form an equilateral triangle.
It shouldn't be too hard, but I can't solve that one just on sight.
As a further simplification, one can observe that:
1. Exactly one spoonful is removed from the wine barrel and added to the tea cup.
2. Exactly one spoonful is removed from the tea cup and added to the wine barrel.
3. From steps 1--2 above, the final volume of the tea cup is the same as the initial volume of the tea cup, and likewise for the wine barrel.
4. Therefore, the net
amount of wine moved from the wine barrel to the tea cup must be the same as the net
amount of tea moved from the tea cup to the wine barrel.
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Here's another tricky geometry problem. (Diagram not to scale.)
been away for today, so no time yet to check.
For that one the trick is to copy and modify the picture which is what makes it deceptive in its difficulty.
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I think it's still a bit tricky if you want to mathematically prove the answer (as opposed to just measuring it with a protractor).
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>>1090445>size doesn't matter
That's what he said!
But at least I got that right then.
Thinking about it a bit while driving. I'm not sure it even matters if it takes physics into account. I'm not sure what I got hung up on because it makes sense in the end.
Anything on the spoon that isn't wine when you go back to the barrel is tea and as such it must necessarily be the same volume as the wine that is now in the cup....?
What happens if we do it again?
Chemistry is weird..>>1090456
Can it be solved by knowing that the angles in a triangle always add up to 180°?>>1090446
If you have three equilateral triangles and want to connect them... No matter how you do it, the triangle in the middle will be the same, right?
Mirrored in some way perhaps, but still? Not sure if it means anything... Just a possible observation.
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Never measure the angles.
Because usually the exercise will just use random angles to trick the contestant.
Though, you could maybe indeed try to draw it out yourself and measure. Which is the long dull way around.
Talking about long dull way, I have this one>>1090446
using the analytical approach.
I probably should check if there's a more conceptual approach, which I sure makes more sense for the exercise.
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ey what the heck goin on in here
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180° for triangles and 360° for rectangles only got me this far.
I'm not a clever pony...>>1090487
The clever ponies are talking math and I'm just thinking about spoons and drawing!
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And that's the cue to nope out before people start bullying me for being a stupid stupid that stupids!
Hey, measuring with a protractor is totally