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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 $a+b+c=d$.
combinatorics
pigeonhole-principle
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.
combinatorics
pigeonhole-principle
In a group of 6 people either we have 3 mutual friends or 3 mutual enemies. In a room of n people?
combinatorics
pigeonhole-principle
Pigeonhole Principle Question: Jessica the Combinatorics Student
combinatorics
pigeonhole-principle
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
elementary-number-theory
pigeonhole-principle
Pigeonhole Principle - Show two subsets have the same age
combinatorics
pigeonhole-principle
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?
discrete-mathematics
pigeonhole-principle
Show that in any set of $2n$ integers, there is a subset of $n$ integers whose sum is divisible by $n$.
combinatorics
modular-arithmetic
pigeonhole-principle
Prove that if 33 rooks are placed on a chessboard, at least five don't attack one another
discrete-mathematics
pigeonhole-principle
Which version of the Pigeonhole principle is correct? One is far stronger than the other
combinatorics
discrete-mathematics
pigeonhole-principle
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.
pigeonhole-principle
Choose 100 numbers from 1~200 (one less than 16) - prove one is divisible by another!
pigeonhole-principle
Prove that if fifteen bishops were placed on a chessboard, then at least two of them attack each other.
pigeonhole-principle
chessboard
Solving a problem using the Pigeonhole principle
combinatorics
discrete-mathematics
pigeonhole-principle
A question related to Pigeonhole Principle
combinatorics
discrete-mathematics
pigeonhole-principle
Prove that every positive integer divides a number such as $70, 700, 7770, 77000$.
number-theory
pigeonhole-principle
Minimum number of holes such that each of 160 pigeons fly in different hole with a condition
combinatorics
pigeonhole-principle
For $a,b$ coprime, there exists positive integers $x,y$ such that $ax-by=1$
elementary-number-theory
proof-explanation
problem-solving
pigeonhole-principle
Prove that if two miles are run in 7:59 then one mile MUST be run under 4:00.
average
pigeonhole-principle
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