##  [Pigeonhole Principle](/pigeonhole-principle) 

  ##  [Pigeonhole Principle](https://natural.quantumdictionary.io/pigeonhole-principle-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A combinatorial principle stating that if n items are placed into m containers and n > m, then at least one container must contain more than one item. Often called Dirichlet's box principle.

 

 

 

 

 





 

 



 ##  [Pigeonhole Principle](https://mathlogic.quantumdictionary.io/pigeonhole-principle-1) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Combinatorial principle stating that when more discrete objects are placed into fewer containers, at least one container must contain more than one object.

 

 

 

 

 





 

 



 ##  [Pigeonhole Principle](https://algebra.quantumdictionary.io/pigeonhole-principle-2) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The combinatorial assertion that if n+1 items are placed into n containers (pigeonholes), then at least one container contains more than one item; more generally, if more items than containers are distributed, some container receives at least the ceiling of items/containers.