Question

Show: For any $n+1$ integers chosen from $[1,2n-1]$, there are $3$ numbers chosen such that the sum of two of them gives us the third number

score 209 · Answer 1 · 2022-01-09 10:05:15

Show: For any $n+1$ integers chosen from $[1,2n-1]$, there are $3$ numbers chosen such that the sum of two of them gives us the third number

score 106 · Answer 2 · 2022-01-18 00:57:12

106

Views

At least how many residents of the country have the same birthday?

Published on 18 Jan 2022 - 0:57

score 240 · Answer 3 · 2022-01-19 15:31:34

240

Views

Application of PHP in Number theory

Published on 19 Jan 2022 - 15:31

score 89 · Answer 4 · 2022-01-20 11:26:28

89

Views

If the the sum of $n$ numbers is $10n$, Prove there exist $k$ numbers that their sum is at least $10k$

Published on 20 Jan 2022 - 11:26

score 71 · Answer 5 · 2022-01-21 12:16:15

71

Views

A Question on the Pigeon Hole Principle

Published on 21 Jan 2022 - 12:16

score 57 · Answer 6 · 2022-01-27 11:30:42

57

Views

$|X| = n \geq 2$. Show that among any $n+2$ subsets of the set $X$, there exist two subsets that have the same number of elements.

Published on 27 Jan 2022 - 11:30

score 28 · Answer 7 · 2022-01-28 13:45:59

28

Views

General properties of "weakly linked" families of sets

Published on 28 Jan 2022 - 13:45

score 51 · Answer 8 · 2022-02-04 23:08:57

51

Views

If $X\subset\mathbb{N}$ such that $\vert\mathbb{N}\setminus X\vert=\aleph_0,$ does $X$ or $\mathbb{N}\setminus X$ contain an arithmetic sequence?

Published on 04 Feb 2022 - 23:08

score 85 · Answer 9 · 2022-02-05 03:08:13

85

Views

Pigeon hole problem unknown pigeons numbers

Published on 05 Feb 2022 - 3:08

score 353 · Answer 10 · 2022-02-10 06:46:50

353

Views

Show that permutations of $n$ have no increasing or decreasing sequences longer than ⌈$\sqrt n$⌉ for any $n$.

Published on 10 Feb 2022 - 6:46

score 106 · Answer 11 · 2022-02-11 12:19:20

Given that the sum of five positive real numbers is 100. Prove that there are two numbers among them whose difference is at most 10 using PHP.

score 81 · Answer 12 · 2022-02-13 13:55:55

81

Views

Pigeonhole principle problem - avoiding a sum in consecutive sets.

Published on 13 Feb 2022 - 13:55

score 67 · Answer 13 · 2022-02-18 14:33:23

67

Views

Points inside unitary circle

Published on 18 Feb 2022 - 14:33

score 122 · Answer 14 · 2022-02-28 08:05:36

122

Views

Pigeonhole $a + b = c + d$

Published on 28 Feb 2022 - 8:05

score 292 · Answer 15 · 2022-03-04 16:31:46

292

Views

To prove that the Fibonacci sequence is periodic modulo m for all positive integers m.

Published on 04 Mar 2022 - 16:31

List Question

Show: For any $n+1$ integers chosen from $[1,2n-1]$, there are $3$ numbers chosen such that the sum of two of them gives us the third number

At least how many residents of the country have the same birthday?

Application of PHP in Number theory

If the the sum of $n$ numbers is $10n$, Prove there exist $k$ numbers that their sum is at least $10k$

A Question on the Pigeon Hole Principle

$|X| = n \geq 2$. Show that among any $n+2$ subsets of the set $X$, there exist two subsets that have the same number of elements.

General properties of "weakly linked" families of sets

If $X\subset\mathbb{N}$ such that $\vert\mathbb{N}\setminus X\vert=\aleph_0,$ does $X$ or $\mathbb{N}\setminus X$ contain an arithmetic sequence?

Pigeon hole problem unknown pigeons numbers

Show that permutations of $n$ have no increasing or decreasing sequences longer than ⌈$\sqrt n$⌉ for any $n$.

Given that the sum of five positive real numbers is 100. Prove that there are two numbers among them whose difference is at most 10 using PHP.

Pigeonhole principle problem - avoiding a sum in consecutive sets.

Points inside unitary circle

Pigeonhole $a + b = c + d$

To prove that the Fibonacci sequence is periodic modulo m for all positive integers m.

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