List questions from pigeonhole-principle

Published on 14 Mar 2019 - 2:40

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Show that there exists $i\in \lbrace 1, 2, 3 \rbrace $ s.t. there exists $a, b\in A_i $ s.t. $a+b\in B $.

Published on 23 Mar 2026 - 14:29

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Examples of the Pigeonhole Principle

Published on 15 Mar 2019 - 20:31

71

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prove something must happen with pigeonhole principle

Published on 18 Mar 2019 - 20:33

159

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When $n$ is an integer such that $n>1$, $S$ is an arbitrary subset of {$1,2,3,...,3n$} and the number of elements of $S$ is $n+2$, prove that

Published on 19 Mar 2019 - 13:16

158

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Prove that $\forall A_k\subset \{1,2,\dots,3n\}$, with $|A_k|=2n$, $\exists (a_i,a_j)\in A_k$ s.t. $a_i-a_j=n-1$

Published on 23 Mar 2019 - 21:26

1.1k

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Given any 2n-1 integers, prove that there are always n of them which add up to a multiple of n

Published on 02 Apr 2019 - 8:37

124

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Solve this Pigeonhole Principle with regards to Divisors and Remainders

Published on 03 Apr 2019 - 19:29

170

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Nine people sat around a table..

Published on 06 Apr 2019 - 3:10

127

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What does it mean if k mod 5 = q mod 5?

Published on 06 Apr 2019 - 19:35

129

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Prove that there is a number that appears at least N times

Published on 08 Apr 2019 - 1:54

425

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Subsets of equal size and equal sum

Published on 10 Apr 2019 - 19:08

245

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Handshake Lemma/Pigeonhole Principle

Published on 11 Apr 2019 - 1:18

532

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Pigeon Hole explanation

Published on 14 Apr 2019 - 8:06

77

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Pigeon hole principle Cartesian product?

Published on 17 Apr 2019 - 2:53

List Question

Pigeonhole principle question 1

Show that there exists $i\in \lbrace 1, 2, 3 \rbrace $ s.t. there exists $a, b\in A_i $ s.t. $a+b\in B $.

Examples of the Pigeonhole Principle

prove something must happen with pigeonhole principle

When $n$ is an integer such that $n>1$, $S$ is an arbitrary subset of {$1,2,3,...,3n$} and the number of elements of $S$ is $n+2$, prove that

Prove that $\forall A_k\subset \{1,2,\dots,3n\}$, with $|A_k|=2n$, $\exists (a_i,a_j)\in A_k$ s.t. $a_i-a_j=n-1$

Given any 2n-1 integers, prove that there are always n of them which add up to a multiple of n

Solve this Pigeonhole Principle with regards to Divisors and Remainders

Nine people sat around a table..

What does it mean if k mod 5 = q mod 5?

Prove that there is a number that appears at least N times

Subsets of equal size and equal sum

Handshake Lemma/Pigeonhole Principle

Pigeon Hole explanation

Pigeon hole principle Cartesian product?

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