Significant Jelly Beans

A quaint little story in the Charlotte Observer [page no longer online] relates how an eight year old, Parker Garrison, spotted a simple arithmetic error in a Discovery Place exhibit that had gone unnoticed by four years of visitors, young and old, educated, and not.

The original exhibit called “Jelly Belly Presents Candy Unwrapped” had a problem for visitors to solve.

How many jelly beans would fit into a particular container.

One example had a container shaped like a half pyramid and told you that a jelly bean has a volume of about 1 cubic cm.

The container’s base measures 46 by 23 cm and its height is 72 cm.

The volume of a pyramid is 1/3 x base area x height.

So, you then had to divide this by 2 since the container is half a pyramid and then multiply your answer by 0.9 to account for spaces between the jelly beans.

The answer should be 22,853.

But, that was patently wrong to young Parker who realized that the base measurements given were for half a pyramid so there was no need to divide by 2 at all.

The story, is like I say, quaint, but him spotting the error is irrelevant, what gives me cause for concern is the fact that the Charlotte Observer tells us there are precisely 22853 jelly beans in the half pyramid. Rubbish, it would be an amazing fluke if there were exactly that number.

Given that jelly beans are a manufactured product of only approximately closed cylindrical shape there’s no way of knowing whether some are a lot less than 0.9 cubic cm and some a lot more. Moreover, they don’t even mention packing density, there are myriad ways these candies could fit into a container some more efficient than others and so some allowing a bigger number contained than others. A really good estimate would be to two or three significant figures at best, so around 23000 plus or minus a couple of hundred, I’d say. But, even then the volume is only given to one significant figure so even that might be pushing it a bit. If one could make such precise estimates of packing based on a unit cell volume known to only one significant figure a lot of materials scientists would be out of work.

And now a word to the wise: If you want some jelly beans don’t go to Discovery Place, buy gourmet jelly beans online and then pig out on those delicious jelly beans when they arrive!