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Twenty distinct integers are chosen from $\{1,2,...,69\}$ and their differences

score 1k · Answer 1 · 2013-02-10 01:23:29

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Twenty distinct integers are chosen from $\{1,2,...,69\}$ and their differences

Published on 10 Feb 2013 - 1:23

score 4.9k · Answer 2 · 2013-02-18 22:27:55

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score 2.6k · Answer 3 · 2013-02-26 06:09:04

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Using the Pigeonhole Principle to show that $2$ of any $n+1$ numbers from $\{1,2,\ldots,2n\}$ sum to $2n+1$

Published on 26 Feb 2013 - 6:09

score 29.1k · Answer 4 · 2013-02-26 17:25:24

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Using Pigeonhole Principle to prove two numbers in a subset of $[2n]$ divide each other

Published on 26 Feb 2013 - 17:25

score 1.3k · Answer 5 · 2013-02-26 18:01:28

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score 119 · Answer 6 · 2013-02-27 03:27:02

119

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score 986 · Answer 7 · 2013-02-28 14:32:21

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score 1.7k · Answer 8 · 2026-03-28 07:16:43

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score 11.3k · Answer 9 · 2013-03-04 16:33:37

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10 people,each of whom ages are $\ge1,\le60$. Show one can always find two groups of people (with no common person) the sum of whose ages is the same.

Published on 04 Mar 2013 - 16:33

score 259 · Answer 10 · 2013-03-05 04:09:22

259

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birthday problem help

Published on 05 Mar 2013 - 4:09

score 3.2k · Answer 11 · 2013-03-06 20:02:39

3.2k

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Choose 38 different natural numbers less than 1000, Prove among these there exists at least two whose difference is at most 26.

Published on 06 Mar 2013 - 20:02

score 268 · Answer 12 · 2026-03-28 10:40:47

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score 105 · Answer 13 · 2013-03-27 17:39:17

105

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Published on 27 Mar 2013 - 17:39

score 380 · Answer 14 · 2013-03-29 04:40:27

380

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Published on 29 Mar 2013 - 4:40

score 145 · Answer 15 · 2020-08-01 15:02:36

145

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If $15$ distinct integers are chosen from the set $\{1, 2, \dots, 45 \}$, some two of them differ by $1, 3$ or $4$.

Published on 01 Aug 2020 - 15:02

List Question

Twenty distinct integers are chosen from $\{1,2,...,69\}$ and their differences

A discrete math riddle

Using the Pigeonhole Principle to show that $2$ of any $n+1$ numbers from $\{1,2,\ldots,2n\}$ sum to $2n+1$

Using Pigeonhole Principle to prove two numbers in a subset of $[2n]$ divide each other

Pigeonhole Principle and Geometry

Counting Subset Properties

pigeonhole principle 20 balls

Guaranteeing an integer lattice point centroid

10 people,each of whom ages are $\ge1,\le60$. Show one can always find two groups of people (with no common person) the sum of whose ages is the same.

birthday problem help

Choose 38 different natural numbers less than 1000, Prove among these there exists at least two whose difference is at most 26.

Ramsey's theory inequality with $t$-subsets

How do I show this, possibly using the pigeonhole principle?

A family of $n$ non-zero vectors of an $(n-1)$-dimensional vector space must be linearly dependent

If $15$ distinct integers are chosen from the set $\{1, 2, \dots, 45 \}$, some two of them differ by $1, 3$ or $4$.

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