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File: 1626833687751.png (162.57 KB, 900x680, 45:34, flutter-tea.png) ImgOps Google

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)


they're equal.


File: 1626835516745.png (7.91 MB, 2796x4096, 699:1024, a8b0d315748782e0dcf7f71746….png) ImgOps Google

You just ruined a perfectly good barrel of wine.


File: 1626849461655.png (151.32 KB, 340x420, 17:21, sluuurp.png) ImgOps Google

seems so.

Mathematics checks out. but I wonder if someone can explain this conceptually.


File: 1626857528403.png (127.36 KB, 768x768, 1:1, gvicw47y37y61.png) ImgOps Google

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.


File: 1626861130890.png (245.39 KB, 425x422, 425:422, is this another interventi….png) ImgOps Google

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.

That's at least already a simplification on what I was thinking.


File: 1626861230886.png (304.09 KB, 498x559, 498:559, well.PNG) ImgOps Google

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.


File: 1626877858260.jpg (96.83 KB, 960x567, 320:189, 1444157529100.jpg) ImgOps Exif Google

Here's another tricky geometry problem.  (Diagram not to scale.)


Why is it inhomogeneous? It can only be solved if it's homogeneous.


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.


File: 1626895137658.png (Spoiler Image, 19.53 KB, 256x515, 256:515, diagram-to-scale.png) ImgOps Google

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).


File: 1626896452310.png (350.23 KB, 2849x3179, 259:289, a1epvh6m0q371.png) ImgOps Google

>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..

Can it be solved by knowing that the angles in a triangle always add up to 180°?

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.


File: 1626896553262.png (163.47 KB, 319x225, 319:225, pinkie G3 that's not my to….png) ImgOps Google

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
using the analytical approach.

I probably should check if there's a more conceptual approach, which I sure makes more sense for the exercise.


File: 1626896731531.png (305.75 KB, 720x820, 36:41, 130085268957.png) ImgOps Google

ey what the heck goin on in here


File: 1626898152748.png (1.59 MB, 2000x2000, 1:1, sketch162689800145.png) ImgOps Google

180° for triangles and 360° for rectangles only got me this far.

I'm not a clever pony...

The clever ponies are talking math and I'm just thinking about spoons and drawing!


File: 1626898941370.png (49.77 KB, 348x320, 87:80, Durr.png) ImgOps Google

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 "elementary geometry"!

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