What is the most efficient way to pack jelly beans in an irregular container?

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Discussion Overview

The discussion revolves around the problem of efficiently packing jelly beans in an irregularly shaped container. Participants explore theoretical approaches to estimating the number of jelly beans that can fit, considering factors such as container shape and packing density. The conversation touches on both mathematical reasoning and practical implications of packing methods.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes a specific irregular container shape (a truncated ellipsoid) and poses the question of how many jelly beans can fit, factoring in empty space between them.
  • Another participant argues that calculating the exact number of jelly beans is impossible due to the infinite arrangements possible, suggesting a method involving the volume of the container and a constant related to packing density.
  • A later reply humorously expresses a desire to focus on the Gaussian distribution of jelly bean packing dynamics.
  • Some participants assert that while it may be challenging, it is not impossible to determine the maximum number of jelly beans that can fit in the jar.
  • There is a distinction made between maximizing packing density and counting randomly packed jelly beans, with implications that packing efficiency may vary significantly.
  • Concerns are raised about the ambiguity in answers due to variations in packing efficiency and the limitations of measuring such efficiency.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of calculating the number of jelly beans that can fit in an irregular container. While some believe it is impossible to determine an exact number due to the infinite arrangements, others argue that it is possible to find the maximum packing density. The discussion remains unresolved with competing perspectives on the topic.

Contextual Notes

Participants highlight the complexity of packing irregular shapes and the influence of random elements on packing efficiency. There is also mention of the potential limitations in constructing a machine to achieve optimal packing patterns.

Mk
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I've been very interested in these since an hour ago, and would like to figure out a few I have devised.

To solve the problems one estimates how many of a geometrical object will fill a cavity in practice. You might be able to find how many melted jelly beans can fit in a jar, but that's not the same as real ones.

The first one I thought of was an oddly shaped jar.

It is a truncated ellipsoid, with dimensions 10" high, 7" at widest, and 4.75" thick. Where is it truncated? Part of it was lopped off, leaving a straight edge that goes halfway up to the equator of it, the top and bottom, and left and right sides were lopped off as well. The flat side on the top and bottom, and the flat side on the left and right are the same.

The third one is a box, which is 10x10x3 inches.

Now, how can we find how many of (the classic) jellybeans can be poured in, making sure to take into account empty space inbetween units? But for an added twist, what about tiny 1x1x1 cm cubes, or Hershey's kisses?
 
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Calculating how many beans can be poured in is impossible; there's an infinite number of ways jellybeans could be arranged in the container. However, if you divide the number of jellybeans by the volume of the container, the result should always be around some value. So it would be best to remember that constant and multiply it by the volume of the container. It'd be interesting to make a Gaussian Curve out of that.
 
I can see it's time to give up my career and dedicate myself to finding the gausian distribution of jelly bean packing dynamics. :-)
 
Werg22 said:
Calculating how many beans can be poured in is impossible; there's an infinite number of ways jellybeans could be arranged in the container. However, if you divide the number of jellybeans by the volume of the container, the result should always be around some value. So it would be best to remember that constant and multiply it by the volume of the container. It'd be interesting to make a Gaussian Curve out of that.

I think I'll do that!
 
Yeah, but it's not impossible to find the number of ways to fit the most number of jellybeans or whatever in the jar.
 
theperthvan said:
Yeah, but it's not impossible to find the number of ways to fit the most number of jellybeans or whatever in the jar.

But is the question, how to maximise jelly bean packing density in an irregular container, or how many randomly packed jelly beans are present in full irregular container.

In the 1st you can work out the optimum packing pattern but would probably never be able to build a machine to pack in that pattern.

In the 2nd there will always be a random element dictating packing efficiency.

Unless the maximum variation in packing efficiency equates to less than the volume of a soingle bean there will always be an ambiguity in the answer.
 

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