Welcome to the Quanta Audio Edition. In each of these bi-weekly episodes, we bring you a story

direct from the Quanta website about developments in basic science and mathematics. I'm

Susan Vallett. If you have more pigeons than pigeonholes, then some pigeonholes will have two pigeons. If you have more pigeons than pigeonholes, then some pigeonholes will have two pigeons.

If you have less pigeons than pigeonholes, then some pigeonholes will be empty.

Obvious statements, perhaps, but behind this so-called pigeonhole principle is a powerful tool used to solve all sorts of computer science problems.

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That's where Editor-in-Chief, Samir Patel, talks to our writers and editors about more of Quanta podcast. That's where editor-in-chief Samir Patel talks to our writers and editors

about more of Quanta's most popular, interesting, and thought-provoking stories.

They see a bird in the hand is worth two in the bush, but for computer scientists, two birds

in a whole are better still.

That's because those cohabiting birds are the protagonists of a deceptively simple mathematical theorem called the pigeonhole principle.

It's easy to sum up in one short sentence.

If six pigeons nestle into five pigeonholes, at least two of them must share a hole.

That's it.

That's the whole thing.

But the pigeonhole principle isn't just for the birds.

Even though it sounds painfully straightforward, it's become a powerful tool for researchers engaged in the central project of theoretical computer science,

mapping the hidden connections between different problems. The pigeonhole principle applies to any situation where items are

assigned to categories, and the items outnumber the categories. For example, it implies that in a

packed football stadium with 30,000 seats, some attendees must have the same four-digit password or pin for their bank cards.

Here, the pigeons are football fans, and the holes are the 10,000 distinct possible four-digit pins.

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