If the average number of envelopes per pigeonhole is , then some pigeonhole will have at least envelopes. Similarly, there must be a pigeonhole with at most envelopes.
Fubini Principle
See also
Dirichlet's Box PrincipleExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Fubini Principle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FubiniPrinciple.html