Question

How one can conclude $S\subseteq \{0,1\}^m$

score 38 · Answer 1 · 2022-03-08 19:04:22

38

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How one can conclude $S\subseteq \{0,1\}^m$

Published on 08 Mar 2022 - 19:04

score 1.2k · Answer 2 · 2026-03-31 12:20:50

1.2k

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Minimum number of balls and pigeonhole principle

Published on 31 Mar 2026 - 12:20

score 194 · Answer 3 · 2026-03-26 01:04:47

194

Views

If for each $j\in\{1,\ldots,m\},\sum_{i=1}^m {x_i}^j = \sum_{i=1}^m {y_i}^j,$ then $(x_i)^{m}_{i=1}$ is a rearrangement of $(y_i)^{m}_{i=1}.$

Published on 26 Mar 2026 - 1:04

score 41 · Answer 4 · 2022-03-15 00:50:09

41

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Two days per year, Combinatorics

Published on 15 Mar 2022 - 0:50

score 43 · Answer 5 · 2022-03-16 06:45:19

43

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Proof using the pigeonhole principle to find two elements, one dividing the other

Published on 16 Mar 2022 - 6:45

score 84 · Answer 6 · 2022-03-18 13:31:13

84

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For every positive integer $k$ not divisible by $101$ there exists $n$ such that the sum $1+k+k^2+...+k^n$ is divisible by 101

Published on 18 Mar 2022 - 13:31

score 130 · Answer 7 · 2022-03-22 05:44:57

130

Views

Least number of numbers to guarantee two sum to $101$

Published on 22 Mar 2022 - 5:44

score 186 · Answer 8 · 2026-04-01 05:05:09

186

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Do rearrangements of $\mathbb{N}$ necessarily have fixed points with respect to placement distance?

Published on 01 Apr 2026 - 5:05

score 131 · Answer 9 · 2022-04-02 14:34:15

131

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Pigeonhole Principle: pick random integer from given set

Published on 02 Apr 2022 - 14:34

score 89 · Answer 10 · 2022-04-02 22:44:00

89

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Given X a set with 100 real numbers and sum 0. Proof that the sum of at least 99 pairs from X is non negative.

Published on 02 Apr 2022 - 22:44

score 121 · Answer 11 · 2022-04-07 16:41:53

121

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Where does the $(c-1)$ come from?

Published on 07 Apr 2022 - 16:41

score 25 · Answer 12 · 2022-04-10 21:21:12

25

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How to prove concerning points on a hemisphere?

Published on 10 Apr 2022 - 21:21

score 60 · Answer 13 · 2022-04-13 11:31:01

60

Views

Pigeonhole principle applications

Published on 13 Apr 2022 - 11:31

score 121 · Answer 14 · 2026-03-26 16:10:07

121

Views

To show that there are two people in the tournament with the same starting hand and position in a Texas Hold'em poker tournament.

Published on 26 Mar 2026 - 16:10

score 600 · Answer 15 · 2022-04-16 12:52:49

$n$ is a integer larger than 1. When picking $n+1$ numbers from the set ${1, 2, \dots, 2n-1}$, you will find a pair whose sum equals $2n$

List Question

How one can conclude $S\subseteq \{0,1\}^m$

Minimum number of balls and pigeonhole principle

If for each $j\in\{1,\ldots,m\},\sum_{i=1}^m {x_i}^j = \sum_{i=1}^m {y_i}^j,$ then $(x_i)^{m}_{i=1}$ is a rearrangement of $(y_i)^{m}_{i=1}.$

Two days per year, Combinatorics

Proof using the pigeonhole principle to find two elements, one dividing the other

For every positive integer $k$ not divisible by $101$ there exists $n$ such that the sum $1+k+k^2+...+k^n$ is divisible by 101

Least number of numbers to guarantee two sum to $101$

Do rearrangements of $\mathbb{N}$ necessarily have fixed points with respect to placement distance?

Pigeonhole Principle: pick random integer from given set

Given X a set with 100 real numbers and sum 0. Proof that the sum of at least 99 pairs from X is non negative.

Where does the $(c-1)$ come from?

How to prove concerning points on a hemisphere?

Pigeonhole principle applications

To show that there are two people in the tournament with the same starting hand and position in a Texas Hold'em poker tournament.

$n$ is a integer larger than 1. When picking $n+1$ numbers from the set ${1, 2, \dots, 2n-1}$, you will find a pair whose sum equals $2n$

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