Fung Kai Liu Man Shek Tong Secondary School - Mathematics

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Pigeonhole Principle


A photo of pigeons in holes.

There are 10 pigeons in 9 holes, so by the pigeonhole principle, at least one hole has more than one pigeon. In this case, both of the top corner holes contain two pigeons. However, the principle says nothing about which holes are empty. In this case, the bottom-left hole is empty.