Can You Solve The Martini Glass Puzzle? A Simple Illusion That Fools Most People

Just how full is your cocktail glass anyway? The answer will surprise you.

Poll
CueMath
DataGenetics

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[webbraham]

I am half way through the video and forgot about the third dimension

[trimeta]

Part of why so many people's intuition was 70% is that in the 2D case, the answer would be 1/sqrt(2), which is 70.7%. And although the wording was very clear that we're interested in the 3D case, the pictures themselves are naturally 2D, which colors our intuition.

[shawty]

as a previous bartender, i knew it was 80% instantly. if you were to pour it into a glass of the same volume but with a cylindrical shape, it would be at the halfway mark.

[zinaidalogunova]

Cone is really good shape of glasses for bars’ owners😀

[wmpowell]

There's an intuitive explanation for the % volume = (% height)^3 formula: as the glass is filled, the shape that the water makes is scaled larger and larger with the tip of the cone anchored in place. Since a cone is three-dimensional, the volume of the cone is scaled in accordance with the cube of the scale factor of the lengths, thus, % volume = (% height)^3.

[piershanson]

One thing about eyballing it is that when doing the poll with just eyballing it, I am naturally inclined to pick the triangle where the orange area is half of the volume rather than remembering that the triangle represents a cone which is what we're actually supposed to eyeball. When I eyball the triangle, 70% is definitely closer to half the area of a triangle, but since the triangle is supposed to be a cone, he 80% actually wins out.

[deemjeffrey]

I guessed 80% bc i’m a bartender.

Literally no calculation, just from working with martinis. Then you started proving it with math and I got so confused haha.

Love your content. Thanks for everything!

[Tea]

Its easy to assume wrong when you're presented with a 2-d image for the options, in a question that wants an answer based on 3 dimensions. What everyone learns in school is to go with what information is presented if the problem doesn't specify any detail.

I know some people will try to be cheeky and say they top of the drawing may imply something, but we all know that can just be there as an artists choice for making any generic 2d cup.

[Zeptonixmusic]

I think that 80% of the height = 50% of the volume is not as mindblowing as 20% of the height being 0.8% of the volume

[paulgreen]

Without using a calculator I realized the answer was the cube root of one half. Then I needed a calculator.

[Clyntax]

A much simpler way to approach this is to observe that both cones are similar. So you want to scale down the larger cone in order to half its volume. Scaling a body does not depend on the shape at all, it can even be done with a cube. If you scale a body in 3D by factor s in every dimension, the volume increases by a factor of s^3. We want to know the scale factor x so that the volume factor is one half: 0.5 = s^3. Therefore, x = 0.5^(1/3) which is almost 0.8 and the answer to the question.
No pi, radius, graphs or complicated formulas needed.

[rorywquin]

I knew the answer immediately.

I came across this in the early 1980s. I was in a bar (in a place called Klerksdorp in South Africa) when two people ordered liqueurs. One wanted a single and the other wanted a double. The barmaid poured their drinks (by eye) into the same size glass. The guy with the double complained because he felt the guy with the single was getting a better deal (more than a single). She got a tot measure & poured a single into it and topped the glass (with the single) up. It came to exactly the same level as the double (she was pretty good at her job).

[neuralwarp]

All the glasses are 100% full. It's just a matter of what they're full of.

[SteinGauslaaStrindhaug]

1:20 Assuming the inside is not a truncated cone, i.e. it's pointy all the way down, the angle should not matter. My intuition says it's around 75%, but it wouldn't surprise me if it's closer to 80%.

[castleanthrax]

The number of comments (on the poll. Not this video) who were saying that it depends on whether the glass is 3d or 2d, astounded me. How anyone could fill a 2d glass with liquid is beyond my understanding.

[ThePowerfulOne]

That explains why my iPhone thinks 80% battery level is considered full!!!

[Inspirator_AG]

*Remember that the real-life counterpart of that diagram is 3-dimensional...*

[suntzupup]

I knew it was 80. Didn't calculate it but I could feel it when I pour and it had pissed me off for years.

[kyyzh]

I remember me and my dad figuring out where you would have to cut a cone into 2 perfect pieces. We also got ~79.4%

[justdilka]

I'm a martini glass half full kinda person