Question

At a party of only 2 people, will these 2 people actually know each other? - Pigeonhole Principle

score 97 · Answer 1 · 2023-03-17 16:08:19

97

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At a party of only 2 people, will these 2 people actually know each other? - Pigeonhole Principle

Published on 17 Mar 2023 - 16:08

score 90 · Answer 2 · 2023-03-19 07:45:07

90

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Pigeonhole principle, a sum question

Published on 19 Mar 2023 - 7:45

score 49 · Answer 3 · 2026-03-25 23:42:43

49

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Fomin et al., Mathematical Circles Chapter 4- Pigeon Hole Principle Problem 12. Max. no. of kings that can be placed so no two put each other in check

Published on 25 Mar 2026 - 23:42

score 77 · Answer 4 · 2023-03-20 11:36:17

77

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paint a board with two colors without repeating the amount painted in each row rows

Published on 20 Mar 2023 - 11:36

score 115 · Answer 5 · 2023-03-21 11:18:43

Given $p - 1$ integers not divisible by an odd prime $p$, we can change signs of some (all or none) of them so that their sum is divisible by $p$.

score 902 · Answer 6 · 2023-03-26 23:00:38

902

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How to prove that, among any +1 distinct odd integers from {1,…,3}, at least one will divide another?

Published on 26 Mar 2023 - 23:00

score 81 · Answer 7 · 2023-03-28 15:16:06

81

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If we remove $\lfloor (2^n-2)/3 \rfloor$ from a set of $\{1,\dots,2^n\}$, there is still a pair of integers $a, b$ such that $a=2b$

Published on 28 Mar 2023 - 15:16

score 278 · Answer 8 · 2026-03-26 14:35:09

278

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Given increasing sequence of numbers, what is guaranteed min length the longest subseq. s.t. differences of terms are either decreasing or increasing?

Published on 26 Mar 2026 - 14:35

score 92 · Answer 9 · 2023-04-07 15:35:30

92

Views

Pigeonhole on sums of subsets from {1,…,99}

Published on 07 Apr 2023 - 15:35

score 282 · Answer 10 · 2023-04-10 04:18:40

282

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Bats in a number of Caves (THE BAT CAVES!!!)

Published on 10 Apr 2023 - 4:18

score 116 · Answer 11 · 2026-03-26 01:23:30

116

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51 points are inside a unit square. How do I prove that a circle with radius 1/7 can always cover 3 of them without using the Pigeonhole Principle?

Published on 26 Mar 2026 - 1:23

score 655 · Answer 12 · 2023-04-14 02:25:21

Choose n+1 numbers from 1 to 2n. Prove that among the chosen numbers, there is always a pair of different numbers (a,b) such that a|b or b|a

score 143 · Answer 13 · 2023-04-19 19:21:37

143

Views

Proof by pigeon hole principle.

Published on 19 Apr 2023 - 19:21

score 179 · Answer 14 · 2026-03-26 09:27:02

179

Views

Given two unbounded subsets $X,Y$ of $\mathbb{R},$ do there exist three points of $X$ whose translation and stretch approximates three points of $Y?$

Published on 26 Mar 2026 - 9:27

score 63 · Answer 15 · 2023-04-24 14:41:31

63

Views

Buss' Polynomial-Size Frege Proof of the Propositional Pigeonhole Principle

Published on 24 Apr 2023 - 14:41

List Question

At a party of only 2 people, will these 2 people actually know each other? - Pigeonhole Principle

Pigeonhole principle, a sum question

Fomin et al., Mathematical Circles Chapter 4- Pigeon Hole Principle Problem 12. Max. no. of kings that can be placed so no two put each other in check

paint a board with two colors without repeating the amount painted in each row rows

Given $p - 1$ integers not divisible by an odd prime $p$, we can change signs of some (all or none) of them so that their sum is divisible by $p$.

How to prove that, among any +1 distinct odd integers from {1,…,3}, at least one will divide another?

If we remove $\lfloor (2^n-2)/3 \rfloor$ from a set of $\{1,\dots,2^n\}$, there is still a pair of integers $a, b$ such that $a=2b$

Given increasing sequence of numbers, what is guaranteed min length the longest subseq. s.t. differences of terms are either decreasing or increasing?

Pigeonhole on sums of subsets from {1,…,99}

Bats in a number of Caves (THE BAT CAVES!!!)

51 points are inside a unit square. How do I prove that a circle with radius 1/7 can always cover 3 of them without using the Pigeonhole Principle?

Choose n+1 numbers from 1 to 2n. Prove that among the chosen numbers, there is always a pair of different numbers (a,b) such that a|b or b|a

Proof by pigeon hole principle.

Given two unbounded subsets $X,Y$ of $\mathbb{R},$ do there exist three points of $X$ whose translation and stretch approximates three points of $Y?$

Buss' Polynomial-Size Frege Proof of the Propositional Pigeonhole Principle

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