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Everyday science

Can you solve this pistachio packing problem?

06 Jul 2024 Michael Banks
Pistachios in a bowl
Tough nut to crack: Pistachios come in different shapes and sizes with the shells being non-symmetric. (Courtesy: Shutterstock/everydayplus)

It sounds like a question you might get in an exam: given a full bowl of N pistachios, what size container do you need for the leftover 2N non-edible shells?

That tasty problem has now been examined by physicists Ruben Zakine and Michael Benzaquen from École Polytechnique in Palaiseau, France.

The issue of how the pistachio shells pack turns out to be a tough nut to crack given that pistachios come in different shapes and sizes with the shells being non-symmetric.

Pistachios are usually served in a bowl as a snack along with another bowl or container in which to place the discarded shells.

Carrying out experiments by placing 613 pistachios in a two litre cylinder, they found, in a nutshell, that the container holding the shells needs to be just over half the size of the original pistachio bowl (for well packed) or three-quarters (for loosely packed).

Zakine and Benzaquen say that numerical simulations on packing pistachios shells could be carried out to compare with the experimental findings.

They also say that the work extends beyond just nuts. “Our analysis can be relevant in other situations, for instance to determine the optimal container needed [for] mussel or oyster shells after a Pantagruelian seafood diner,” they write.

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