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For this, you need nothing more than the “pigeonhole principle,” also called “Dirichlet’s principle.”

The pigeonhole principle is usually attributed to Peter Gustav Lejeune Dirichlet, who lived about 200 years after Leurechon.

Holmes, I., Harris, K. & Quince, C. Dirichlet multinomial mixtures: generative models for microbial metagenomics.

This bit of common sense, sometimes termed the pigeonhole or Dirichlet drawer principle, can occasionally be used to derive claims that are not so obvious.

To help explain what the researchers were doing — their study involved something called a “Dirichlet process Gaussian Mixture Model” — I called the lead author, Patrick Shafto.