Pigeons and Lemmas

Pigeons are generating a simple but powerful principle, the Pigeon Hole Principle. It implies a cluster of important Lemmas and Theorems. Misra’s Lemma in the figure was in fact originated as a puzzle by Kolmogorov, according to Levin; it is with several other interesting ‘amuses’ and their proofs collected on the website of Yayadev Misra. The name mulitsets is coined by N.G. (Dick) de Bruijn, according to Donald Knuth.