New posts in Pigeonhole Principle

On division by gcd

A "distinguishing" family of subsets

Is it possible to find 2014 distinct positive integers whose sum is divisible by each of them?

Given three permutations of $\{1,2,\dots,n^3+1\}$, prove two of them have a common subsequence of length $n+1$.

Prove that given any five integers, there will be three for which the sum of the squares of those integers is divisible by 3.

A standard and rigorous proof using the pigeonhole principle

$7$ fishermen caught exactly 100 fish and no two had caught the same number of fish. Then there are three who have together captured at least 50 fish.

Elementary number theory in sets

The pigeonhole principle and a professor who knows $9$ jokes and tells $3$ jokes per lecture

Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n