Friday, 11 July 2014

Guessing jelly beans in a jar by volume

Ever since reading an article about the packing density of M&Ms and how to calculate very closely how many fit into a given volume, I've been excited to give the technique a try on a real contest. There have been two contests I've encountered since then, but in both cases the jar was filled with jelly beans, not M&Ms. The technique still stands, but I have always found myself trying to look up the packing factor of jelly beans rather than referencing the M&Ms paper. The best answers I can find online don't state the actual packing factor, but give advice on how to calculate it. You would think, at some point, someone would have figured this out, but apparently not. Perhaps, then, I can be the first to publish a jelly bean packing factor calculation.

In the most recent competition, I was off by 4 beans. I guessed at 2cm^3 per bean and 80% packing efficiency. This means you just have to multiply the volume of the container (in cubic centimetres or millilitres) by 0.4 and you'll get a pretty good estimate. The container in the last contest I encountered was 2 litres, so I guessed 800 beans. The answer was 796 and, unfortunately, someone else had guessed 795, so they won.

Mokalus of Borg

PS - Note that these are "standard" jelly beans, about 2cm long.
PPS - The much smaller "Jelly Belly" brand or any other size won't work with this calculation.

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