My discrete mathematics book gives the following definition for the pigeonhole principle:(adsbygoogle = window.adsbygoogle || []).push({});

If m objects are distributed into k containers where m > k, then one container must have more than [itex]\lfloor[/itex][itex]\frac{m-1}{k}[/itex][itex]\rfloor[/itex] objects.

It then states as a corollary that the arithmetic mean of a set of numbers must be in between the smallest and largest numbers of the set. No proof is given, it pretty much just says "well it's just obvious that this is the case."

I think it is obvious that the arithmetic mean of a set of numbers is in between its smallest and largest values. What isn't obvious to me is how their definition of the pigeonhole principle leads to the corollary. Can anyone help me out?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Pigeonhole Principle and the Arithmetic Mean

Loading...

Similar Threads - Pigeonhole Principle Arithmetic | Date |
---|---|

A Convolution, singularity, kernel, principle values, linear stability analysis, quadrature points | May 21, 2017 |

I Sum principle proof: discrete mathematics | Oct 8, 2016 |

What is the principle of algebra called? | Sep 13, 2015 |

Pigeonhole Principle question | Mar 31, 2011 |

Advanced Pigeonhole principle | Jul 5, 2010 |

**Physics Forums - The Fusion of Science and Community**