New posts in Pigeonhole Principle

"Math Lotto" Tickets - finding the minimum winning set

A simple graph must have at least one pair of vertices whose degrees are equal.

Does there exist a bijection that is not eventually equal to the identity, but has a finite number of "crosses"?

Among any $9$ real numbers, two satisfy $0 < \frac{x-y}{1+xy} < \sqrt{2} - 1$

Find smallest $n$ fulfilling requirement

How to use Pigeon Hole Principle here?

Clarification on pigeonhole principle for case of choosing $k$ elements from a set such that $2$ elements from the subset sum to a particular number

If $15$ distinct integers are chosen from the set $\{1, 2, \dots, 45 \}$, some two of them differ by $1, 3$ or $4$.

How to prove that any number from $0$ to $\frac{n(n+1)}{2}$ can be obtained as sum of subset of set {$1,2,3, ... ,n$}

Prove or disprove that in an 8-element subsets of $\{1,2…,30\}$ there must exist two $4$-element subsets that sum to the same number.