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

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In summary, the conversation discusses different methods for calculating the number of jellybeans or other objects that can fit into a container. It is mentioned that while it is impossible to determine the exact number due to the infinite ways of arranging the objects, a constant can be used to estimate the amount. The idea of creating a Gaussian Curve to represent the packing dynamics is also brought up. The conversation concludes with a discussion on the ambiguity of finding the optimum packing pattern in an irregular container.
  • #1
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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  • #2
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.
 
  • #3
I can see it's time to give up my career and dedicate myself to finding the gausian distribution of jelly bean packing dynamics. :-)
 
  • #4
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!
 
  • #5
Yeah, but it's not impossible to find the number of ways to fit the most number of jellybeans or whatever in the jar.
 
  • #6
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.
 

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

1. How do you solve a jellybean jar problem?

The most common approach to solving a jellybean jar problem is by using a basic counting strategy. First, count the number of jellybeans in a small portion of the jar. Then, estimate the number of portions in the whole jar and multiply that by the number of jellybeans in the small portion. This will give you an estimate of the total number of jellybeans in the jar.

2. What is a reasonable estimate for the number of jellybeans in a jar?

A reasonable estimate for the number of jellybeans in a jar can vary depending on the size of the jar and the size of the jellybeans. However, a good starting point is to count the number of jellybeans in a small portion of the jar and use that number to estimate the total amount. It's also important to take into account any empty space in the jar that may affect the estimate.

3. How accurate are estimates for jellybean jar problems?

The accuracy of estimates for jellybean jar problems can vary depending on the counting strategy used and the consistency of the jellybean sizes. While estimates may not be exact, they can provide a close approximation of the total number of jellybeans in the jar.

4. Are there any other methods for solving jellybean jar problems?

Aside from using a basic counting strategy, there are other mathematical approaches that can be used to solve jellybean jar problems. Some methods involve using statistics or probability to make a more accurate estimate of the number of jellybeans in the jar.

5. Can jellybean jar problems be used in real-world applications?

Yes, jellybean jar problems can be used in real-world applications as a way to teach basic counting and estimation skills. They can also be used in industries such as manufacturing and retail to estimate the number of items in a larger batch based on a smaller sample.

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