Question

For any sequence of $n$ integers, there exists a subsequence whose sum is divisible by $n$.

score 5.6k · Answer 1 · 2014-03-05 03:34:06

5.6k

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For any sequence of $n$ integers, there exists a subsequence whose sum is divisible by $n$.

Published on 05 Mar 2014 - 3:34

score 1.9k · Answer 2 · 2014-03-08 01:31:11

1.9k

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Rotating a table so that at least two name cards are correct

Published on 08 Mar 2014 - 1:31

score 4.5k · Answer 3 · 2014-03-08 04:35:33

4.5k

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The Probabilistic Pigeon Hole Principle

Published on 08 Mar 2014 - 4:35

score 88 · Answer 4 · 2014-03-08 23:44:38

88

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$[x-\frac{1}{n}, (n-1)x+\frac{1}{n}]$ contains an integer $\forall x\in \mathbb{R}$ and $\forall n\in \mathbb{N}$

Published on 08 Mar 2014 - 23:44

score 256 · Answer 5 · 2014-03-09 09:53:40

Prove:that in any set of 1009 positive integers exits two numbers $a_i$ and $a_j$ such that $a_i-a_j$ or $a_i+a_j$ is divisible by 2014

score 2.6k · Answer 6 · 2017-04-10 04:54:07

2.6k

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Proving subset sums with the pigeon hole principle

Published on 10 Apr 2017 - 4:54

score 82 · Answer 7 · 2017-04-10 22:52:26

82

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Pigeonhole principle to prove distance between two players

Published on 10 Apr 2017 - 22:52

score 110 · Answer 8 · 2017-04-12 03:32:10

110

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Pigeonhole Principle involving contradiction

Published on 12 Apr 2017 - 3:32

score 164 · Answer 9 · 2026-03-26 11:17:21

164

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pigeonhole principle proof for 10 kings in a chessboard

Published on 26 Mar 2026 - 11:17

score 111 · Answer 10 · 2017-04-13 12:58:12

111

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pigeonhole principle proof for division by $20$

Published on 13 Apr 2017 - 12:58

score 229 · Answer 11 · 2017-04-24 05:24:16

229

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Pigeon Hole problem on any set of distinct integers

Published on 24 Apr 2017 - 5:24

score 3.5k · Answer 12 · 2017-04-26 08:45:20

3.5k

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Pigeonhole principle: prove that any set of $n+1$ integers from $\{1,2,...,2n\}$ has two consecutive integers differ by one.

Published on 26 Apr 2017 - 8:45

score 148 · Answer 13 · 2017-04-27 12:33:08

148

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Prove there exists two sub-sets of indices $I,J\subseteq [2n]$ such that $\sum_{i\in I}a_i=\sum_{j\in J}b_j$

Published on 27 Apr 2017 - 12:33

score 127 · Answer 14 · 2017-04-29 06:29:27

127

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How to prove that there is at least 1 triangle of same colour?

Published on 29 Apr 2017 - 6:29

score 1.8k · Answer 15 · 2017-05-01 21:35:21

1.8k

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How to solve this Pigeon-hole Problem.

Published on 01 May 2017 - 21:35

List Question

For any sequence of $n$ integers, there exists a subsequence whose sum is divisible by $n$.

Rotating a table so that at least two name cards are correct

The Probabilistic Pigeon Hole Principle

$[x-\frac{1}{n}, (n-1)x+\frac{1}{n}]$ contains an integer $\forall x\in \mathbb{R}$ and $\forall n\in \mathbb{N}$

Prove:that in any set of 1009 positive integers exits two numbers $a_i$ and $a_j$ such that $a_i-a_j$ or $a_i+a_j$ is divisible by 2014

Proving subset sums with the pigeon hole principle

Pigeonhole principle to prove distance between two players

Pigeonhole Principle involving contradiction

pigeonhole principle proof for 10 kings in a chessboard

pigeonhole principle proof for division by $20$

Pigeon Hole problem on any set of distinct integers

Pigeonhole principle: prove that any set of $n+1$ integers from $\{1,2,...,2n\}$ has two consecutive integers differ by one.

Prove there exists two sub-sets of indices $I,J\subseteq [2n]$ such that $\sum_{i\in I}a_i=\sum_{j\in J}b_j$

How to prove that there is at least 1 triangle of same colour?

How to solve this Pigeon-hole Problem.

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