If you put them in the trash there's 0

1. Set lower bound by counting how many are visible in the photo
2. Grow disinterested
3. Guess some number above the result from step 1

For a tapered section like that, you could estimate bottom and top layers and then average them. Then estimate height and multiply. You'd want to include an overlap factor as the roughly spherical nuts would settle in between each other somewhat. I'd imagine there's some accepted value out there for that.

Start with the bottom, count how many are visible on the lowest layer. This gives you half the circumference of the lower end.

Repeat for the highest part of the cup that is still cup, not above the line.

Multiply each of these by 2 and you have the circumferences of each end of the cut cone.

Rearrange the circle area formula to get the radius from circumference and you have the radius of each end of the cone.

Now use the cut cone formula to calculate the volume in terms of hazelnuts.

Next, take the radius of the top circle and estimate how far above that the highest nut is. Use whatever formula seems more appropriate, in this case maybe just a right angle triangle formula with a full rotation, to estimate the volume of the top.

Sum that together with the conic volume and you have a good estimate.

My estimate, at least 3 hazelnuts.

Good luck

Roughly a truncated cone with diameters ~7 nuts and ~9 nuts, and the cup is ~12 nuts high (loose guesses, it is hard to tell due perspective and nuts of different sizes). Throw in an extra layer to account for the heap at the top (which is a dome taller than 1 hazelnut, but treating it as a shorter but full layer should give some error cancellation) to give a height of 13. The volume of a truncated cone of those dimensions is ~657 cubic hazelnut diameters. Random sphere packing is 64% space-efficient (though wall effects should decrease this number) giving a total of 420 nuts (nice).

Multiple edits for clarity and typos.

Volume of glass

Volume of hazelnuts (median)

Packing efficiency of spheres in a cylinder

Do some math

Be wrong by an order of magnitude because all the little hazelnuts are concealing one giant one

licks screen

210

Vibes. I look at it and try to guess and submit a number within 5 or 10 seconds. It may not be as accurate but I feel like I get more benefit training my ability to estimate at a glance than I do training my ability to do math and spatial reasoning assisted by math. Im already really good at math and math assisted spatial reasoning

Find a cup that is similarly shaped and sized, fill it with hazelnuts and then count it manually

My method was that I waited for @m0darn@lemmy.ca to do the work and used it as a baseline. I got 8 away.

I did

V=pi×r²×h

and estimated:

r=4 (from some at the top left)

h=12

This gave 603. The link said too high, so realized I'd neglected packing factor. Google said that spheres typically pack at 64% efficiency, so I guessed 386. Too low.

Imagej

In arbitrary units, I need in pixels estimations for:

Height of the vase H

Top diameter of the vase Dt

Bottom diameter of the vase Db

Mean diameter of a hazelnut Dh (measuring a few of them)

Packaging factor F... something arround .6? I'm sure there is a better way of estimating it. Like counting air and hazelnut areas on the image but I'm not sure how to correlate 2D to 3D in this case.

The volume of the vase is Vv (H,Dt,Db)

The volume of a single hazelnut Vh (Dh)

N = Vv F / Vh

Zero.

Ceci ne sont pas noisettes.

I counted 11 down and 7 across, so I assumed the radius is 3.5 hazelnuts and the height eleven, making pi r² h = 423 hazelnuts. that is, if they haven't snuck in any walnuts.

The cup is about 13 hazelnuts high. The top circumference looks like it could hold about 24, the bottom about 20, so I’ll average that to 22.

13*22=286

Someone say a God Damn number. _

I would look at them and pull a number out of my ass.

This is a 2D image of a cup of hazelnuts. The number is just the ones you can see. The ones you can't see aren't part of the image.

All of them are in the cup.

Totally unrelated: Now I have the urge for a doner kebab.

Empty the cup and then count them all

i'll eat one every day and tell you how many years are inside the jar

For me, it would be more about figuring out the rough volume. So, like, you look at a hazelnut, it appears to be about a half-inch spherical value. There seem to be about 6 wide across the bottom, so you could assume that the bottom is somewhere around three inches wide. The top is probably closer to about 5 inches wide. And the height is going to be something like 6 inches.

This is also using rough guesstimation from my own personal knowledge of cups.

So with that information I would use what I remember of the cylinder formula, which is pi times diameter times height I think.

And average the two diameters for a four, so you would go four times six times pi is about 75 cubic inches of volume. Each hazelnut uses about 3/4 of an inch of volume so I would guess there are about 100 hazelnuts in the cup.

That being said, the question is not, what is the correct way to guess it, just how would I do it, and this is how I would do it.

I'm going to guess the cup is around 12 nuts high and 5 nuts in diameter at the center.

Let's assume it's a cylinder to get the volume (2/5)^2 * pi * 12 as the volume or around 236 nuts.

The packing density of a sphere is 74% but the edges do play a factor so nudge it down by a bit to get 70%

So I'm going to guess 165 nuts.

I got it laughably wrong

Count the visible ones and multiply by pi. Not that accurate, considering the shape of the glass and the top of the nut stack, but it's about as close as I can be arsed calculating now. I refuse to be nerd sniped today, so a ballpark figure will have to suffice.

I'd ask a couple thousand people to guess in private. So the most popular answer would probably be either surprisingly close to correct or Cuppy McHazelnutface.

Avarage all the guesses of others. (Doesn't work if they also use this method)

Weigh 10 hazelnuts, weigh all hazelnuts, do basic math.

this was fun. thanks. I like the stats on that website

None, that's a jar.

None, those are pretzel bites

, side view