A Problem About Pigeons Powers Complexity Theory
(quantamagazine.org)
They say a bird in the hand is worth two in the bush, but for computer scientists, two birds in a hole 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.
They say a bird in the hand is worth two in the bush, but for computer scientists, two birds in a hole 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.