The Generalized Pigeonhole Principle




 If N objects are placed into K boxes , then there is at least one box containing at least 

\[\left\lceil {\frac{N}{K}} \right\rceil \] objects .

( Notice that\[\left\lceil r \right\rceil \] is the ceiling of r )

Example: 
Among 100 people , there are at least \[\left\lceil {\frac{{100}}{{12}}} \right\rceil = 9\] who were born in the same month .

Post a Comment

Please Select Embedded Mode To Show The Comment System.*

Previous Post Next Post