Question

Integer pick with pigeon hole principle

score 525 · Answer 1 · 2026-04-08 18:04:49

525

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Integer pick with pigeon hole principle

Published on 08 Apr 2026 - 18:04

score 332 · Answer 2 · 2026-04-13 20:58:38

332

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IMO $2014$ shortlist question. PigeonHole-Principle to solve?

Published on 13 Apr 2026 - 20:58

score 188 · Answer 3 · 2026-04-14 05:02:53

188

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Seat n people in 4 benches

Published on 14 Apr 2026 - 5:02

score 590 · Answer 4 · 2026-04-16 09:15:52

590

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What is the greatest number of stickers she could take out of the bag if she stops when she has $3$ stickers of the same colour?

Published on 16 Apr 2026 - 9:15

score 163 · Answer 5 · 2026-04-15 08:37:29

163

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Prove that for a family of $100n$ subsets of a $[n]$ such that each subset has size $m$, there exists two whose intersection is at least $m^2/10n$.

Published on 15 Apr 2026 - 8:37

score 1.6k · Answer 6 · 2026-05-10 12:30:08

1.6k

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Prove that a graph with $100$ vertices with each edge having degree at most $4$ contains an empty graph of order $20$.

Published on 10 May 2026 - 12:30

score 441 · Answer 7 · 2026-05-10 14:52:33

441

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There is two triangles with common edge in graph $\Gamma$

Published on 10 May 2026 - 14:52

score 141 · Answer 8 · 2026-04-15 13:53:39

141

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To prove there exists a particular format of multiple

Published on 15 Apr 2026 - 13:53

score 235 · Answer 9 · 2026-04-12 19:20:04

235

Views

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Published on 12 Apr 2026 - 19:20

score 482 · Answer 10 · 2026-04-14 14:30:09

482

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In every set of 100 integers, there exist two whose difference is a multiple of 37.

Published on 14 Apr 2026 - 14:30

score 9.1k · Answer 11 · 2026-04-12 08:20:58

9.1k

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The pigeonhole principle and a professor who knows $9$ jokes and tells $3$ jokes per lecture

Published on 12 Apr 2026 - 8:20

score 78 · Answer 12 · 2026-04-10 21:13:55

78

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Pigeonhole principle for boxes

Published on 10 Apr 2026 - 21:13

score 157 · Answer 13 · 2026-04-12 05:28:46

157

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Published on 12 Apr 2026 - 5:28

score 91 · Answer 14 · 2026-04-09 07:42:38

91

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Choosing a balanced subsequence

Published on 09 Apr 2026 - 7:42

score 122 · Answer 15 · 2026-04-12 08:54:51

122

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Can I use the pigeon-hole principle to show that $a^2-2b^2=p$ has a solution?

Published on 12 Apr 2026 - 8:54

List Question

Integer pick with pigeon hole principle

IMO $2014$ shortlist question. PigeonHole-Principle to solve?

Seat n people in 4 benches

What is the greatest number of stickers she could take out of the bag if she stops when she has $3$ stickers of the same colour?

Prove that for a family of $100n$ subsets of a $[n]$ such that each subset has size $m$, there exists two whose intersection is at least $m^2/10n$.

Prove that a graph with $100$ vertices with each edge having degree at most $4$ contains an empty graph of order $20$.

There is two triangles with common edge in graph $\Gamma$

To prove there exists a particular format of multiple

Proof of simple graph using pigeonhole theorem

In every set of 100 integers, there exist two whose difference is a multiple of 37.

The pigeonhole principle and a professor who knows $9$ jokes and tells $3$ jokes per lecture

Pigeonhole principle for boxes

Putnam Question (Pigeonhole Principle on divisibility of sequences)

Choosing a balanced subsequence

Can I use the pigeon-hole principle to show that $a^2-2b^2=p$ has a solution?

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