New posts in pigeonhole-principle

Let $T$ be any subset of $\{1,2,3,...,100\}$ with $69$ elements. Prove that one can find four distinct integers such that $a+b+c=d$.

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.

In a group of 6 people either we have 3 mutual friends or 3 mutual enemies. In a room of n people?

Pigeonhole Principle Question: Jessica the Combinatorics Student

Show that any set of 7 distinct integers includes two integers $x$ and $y$, such that either $x-y$ or $x+y$ is divisible by 10

Pigeonhole Principle - Show two subsets have the same age

What is the smallest number of people in a group, so that it is guaranteed that at least three of them will have their birthday in the same month?

Show that in any set of $2n$ integers, there is a subset of $n$ integers whose sum is divisible by $n$.

Prove that if 33 rooks are placed on a chessboard, at least five don't attack one another

Which version of the Pigeonhole principle is correct? One is far stronger than the other

Assume that we have six positive real numbers whose sum is 150. Prove that there exist two of them whose difference is less than 10.

Choose 100 numbers from 1~200 (one less than 16) - prove one is divisible by another!

Prove that if fifteen bishops were placed on a chessboard, then at least two of them attack each other.

Solving a problem using the Pigeonhole principle

A question related to Pigeonhole Principle

Prove that every positive integer divides a number such as $70, 700, 7770, 77000$.

Minimum number of holes such that each of 160 pigeons fly in different hole with a condition

For $a,b$ coprime, there exists positive integers $x,y$ such that $ax-by=1$

Prove that if two miles are run in 7:59 then one mile MUST be run under 4:00.