Linked from

The 30 pages that link to Pigeonhole principle, each with the reason it gives.

• CombinatoricsRelated: It proves existence without requiring an exact count or explicit construction.

• Data compressionRelated: It proves that no lossless method can make every possible input shorter.

• Lossless compressionRelated: It proves that no lossless method can shorten every possible input of a fixed length.

• Finite setRelated: It follows from the impossibility of injecting a larger finite set into a smaller one.

• Injective functionRelated: It proves collisions must occur when there are more inputs than available outputs.

• Ramsey theoryRelated: Ramsey arguments repeatedly use forced repetition as a starting point.

• Surjective functionRelated: For finite sets, cardinality comparisons often decide whether a function can be surjective.

• Diophantine approximationRelated: Its counting argument yields Dirichlet-type rational approximation bounds.

• DiagonalizationCompared with: It proves some impossibility results by counting, rather than constructing a missing diagonal object.

• Recreational mathematicsRelated: It yields striking existence proofs from deceptively simple counting arguments.

• Birthday ProblemNarrower topic: It guarantees a match once a group exceeds the number of possible birthdays.

• Diagonal argumentCompared with: It proves some counting impossibilities directly, whereas diagonal arguments construct an object missing from a list.

• Schur's theoremRelated: Finite colorings force repeated colors among strategically chosen integer sums.

• Dirichlet's approximation theoremRelated: Partitioning fractional parts into intervals produces two whose difference yields the required approximation.

• Even numberRelated: Parity can sharpen counting arguments by separating objects into two classes.

• Pumping lemma for regular languagesRelated: A long accepting run visits some state more than once, creating a repeatable segment.

• Ramsey's theoremRelated: Its finite form supplies the basic repetition idea behind Ramsey arguments.

• Mathematical puzzleRelated: It yields short solutions to puzzles about repetition and allocation.

• Discrete mathematicsRelated: It yields existence proofs from simple comparisons of finite quantities.

• Erdős–Szekeres theorem (monotone subsequences)Related: The proof assigns each term a pair of subsequence lengths; too many terms force a repeated pair.

• Siegel's lemmaRelated: Siegel's lemma can be proved by mapping many bounded integer vectors to fewer possible equation outputs.

• Combinatorial principlesBroader topic: It guarantees collisions when objects are assigned to too few categories.

• Erdős–Gyárfás conjectureRelated: Proof strategies can use repeated neighborhoods or path lengths to force a cycle.

• Friends and strangers theoremRelated: Among five relationships from one person, at least three share the same friend-or-stranger status.

• Herzog–Schönheim conjectureRelated: The conjecture seeks a repeated index among the subgroups in a partition.

• Infinite monkey theoremCompared with: It gives deterministic guarantees from finite counting, unlike this probabilistic result.

• Law of Truly Large NumbersCompared with: It guarantees a collision by counting alone, while rare-event accumulation usually gives only a probability.

• Lonely runner conjectureRelated: Elementary proofs use it to force gaps among runners’ positions.

• Steiner–Lehmus theoremRelated: A classic proof uses an auxiliary construction and a contradiction with this counting principle.

• Thue's lemmaNarrower topic: Elementary proofs of lattice-point existence often reduce to this broader counting idea.