• anyhow2503@lemmy.world
    8·
    24 days ago
    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
  • rowinxavier@lemmy.world
    7·
    24 days ago

    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

  • m0darn@lemmy.ca
    5·
    24 days ago

    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.

  • neidu3@sh.itjust.worksEnglish
    2·
    24 days ago

    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.

  • TheCriticalMember@aussie.zoneEnglish
    2·
    24 days ago

    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.

    • CmdrShepard49@sh.itjust.works
      2·
      24 days ago

      This is what I did. Roughly 5 wide at the bottom and 7 wide at the top or roughly 12 nuts per layer average. Then the stack appears to be about 12 nuts high so 144 total and maybe round up to 150 since it’s heaping at the top.

      Edit: I didn’t initially see OP’s link to the site and I call complete bullshit on that ‘correct’ answer without seeing them poured out and counted on video. According to it, my answer is off by several hundred.

      • brian@lemmy.ca
        2·
        24 days ago

        Not sure where you’d land at 12 nuts per layer on average. If you go off 5 nuts “wide” as your diameter you’d end up with at least 20 nuts at the bottom layer (area = π(5/2)² = 19.6).

        • CmdrShepard49@sh.itjust.works
          1·
          24 days ago

          I did 5 wide at the bottom and 7 wide at the top. 5x2 and 7x2 =24/2 (average) = 12 per layer. I now see how this isnt exactly correct as it’s a circle but the ‘proper’ answer puts it at 36 per layer which doesnt seem correct either.

        • CmdrShepard49@sh.itjust.works
          1·
          24 days ago

          Only when it jives with a sensible guesstimation.

          Without outright spoiling the answer, according to the site, roughly every visible hazelnut in the image makes up just 16% of the total. If my guess of 12 layers is roughly accurate, every visible hazelnut only makes up two layers of the total which doesnt seem correct.

          Considering this is a user submitted puzzle with zero verification (as far as I know), the simplest answer is that they gave a fake/incorrect number.

  • Siegfried@lemmy.world
    1·
    24 days ago

    Can we interact with it? What about weighting it, subtracting the mass of the vase and dividing by whatever the mean weight of a hazelnut is?

    • wjrii@lemmy.world
      2·
      24 days ago

      I don’t math so good, so I roughly counted layers and used the formula for area of a circle, reduced slightly for gaps. First guess was a good 10%-15% off but got within 12 on the second. Then I seriously overcorrected on my third.

      • ryannathans@aussie.zone
        3·
        24 days ago

        Nice work. Cylinder volume is just area of circle multiplied by height, nothing too fancy. Imagine a circle being extruded by one dimension (height)

  • bizarroland@lemmy.worldEnglish
    1·
    24 days ago

    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.

    • Skua@kbin.earth
      1·
      24 days ago

      I think that this is more or less the approach I would take, but you shouldn’t worry about the actual diameter of anything. It’s not important, after all - if everything was scaled up twice as big, the answer would be the same. Just call the diameter of the cup a nice round number and then see how the hazelnuts compare to it. In this case I think there’s about five hazelnut widths to the glass, so I’m gonna call the glass diameter 50, the nuts 10, and the glass height 80.

      You’ll need to change your formulae, though. pi*d is the circumference of a circle, but we need the area here, so pi*r*r (and then multiply by height for volume). That gives me 157,050 whateverunits cubed for the volume of the cup. For a sphere it’s (4/3)*pi*r*r*r, so 524 for the hazelnuts. Now, I know that spheres don’t pack perfectly into a volume, but I don’t remember the factor even for optimal packing, so I’m just gonna take a wild guess and say that 70% of the internal volume of the cup is actually occupied by hazelnuts. That gives me… 209 hazelnuts in the cup. Which seems worse than your answer on a gut level, but I can count 86 visible ones so it’s maybe actually not bad

      Checking my results

      Hah, I was way off too

  • Alexstarfire@lemmy.world
    1·
    24 days ago

    Find volume of one of them (can probably be found online), calculate volume of container, see how many could fit if you didn’t have to worry about physics, take a bit less than that.

    There are some outside the container but I still think the amount of empty space is greater than that.

  • driving_crooner@lemmy.eco.br
    1·
    24 days ago

    For this one I would count half of the from, half of the top, multiply them, the multiply by 4, the subtract the 10%.

    28 front 8 top (28x8x4)×(0.9) = 691.2 ~ 691