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New posts in pigeonhole-principle
Are there rigorous formulation and proof of the pigeonhole principle?
combinatorics
pigeonhole-principle
if there are 5 points on a sphere then 4 of them belong to a half-sphere.
geometry
pigeonhole-principle
Chess Master Problem
combinatorics
pigeonhole-principle
Prove using induction that from a set of $n+1$ numbers from $\{1,2,..2n\}$, at least one number will evenly divide another.
induction
pigeonhole-principle
Prove that at a party of $25$ people there is one person knows at least twelve people.
combinatorics
discrete-mathematics
graph-theory
contest-math
pigeonhole-principle
The pigeonhole principle and a professor who knows $9$ jokes and tells $3$ jokes per lecture
combinatorics
permutations
combinations
pigeonhole-principle
Using Pigeonhole Principle to prove two numbers in a subset of $[2n]$ divide each other
combinatorics
pigeonhole-principle
Of any 52 integers, two can be found whose difference of squares is divisible by 100
elementary-number-theory
discrete-mathematics
pigeonhole-principle
A discrete math riddle
discrete-mathematics
puzzle
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.
combinatorics
discrete-mathematics
contest-math
pigeonhole-principle
discrete-optimization
100 Soldiers riddle
combinatorics
pigeonhole-principle
puzzle
inclusion-exclusion
What is your favorite application of the Pigeonhole Principle?
big-list
education
pigeonhole-principle
A natural number multiplied by some integer results in a number with only ones and zeros
elementary-number-theory
algorithms
pigeonhole-principle
For an irrational number $\alpha$, prove that the set $\{a+b\alpha: a,b\in \mathbb{Z}\}$ is dense in $\mathbb R$ [closed]
real-analysis
irrational-numbers
pigeonhole-principle
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