Question

Prove that it in a regular 100-gon where each vertices is colored in one of 10 colors, there exists a rectangle colored in at most 2 colors.

score 92 · Answer 1 · 2026-03-31 10:13:54

92

Views

Prove that it in a regular 100-gon where each vertices is colored in one of 10 colors, there exists a rectangle colored in at most 2 colors.

Published on 31 Mar 2026 - 10:13

score 216 · Answer 2 · 2021-03-28 20:51:01

Prove that if n + 1 distinct numbers are selected from 1 to 2n - 1, then there is always a number in selected ones that is sum of two other selected

score 1.4k · Answer 3 · 2021-03-31 15:19:55

Given a list of integers from $1$ to $1000$ inclusive, what is the smallest $k$ numbers you pick such that it has $3$ consecutive numbers?

score 54 · Answer 4 · 2026-04-02 12:30:48

54

Views

If $X$ is a subset of $A$ with more than $n$ elements, then there exist $a,b \in X$ such that $ a \mid b $ or $b \mid a$.

Published on 02 Apr 2026 - 12:30

score 67 · Answer 5 · 2021-04-02 15:24:59

67

Views

Probability of birthday

Published on 02 Apr 2021 - 15:24

score 539 · Answer 6 · 2026-03-26 04:36:22

539

Views

Let $B\subset A = \{1,2,3,...,99,100\}$ and $|B|= 48$. Prove that exist $x,y\in B$, $x\ne y$ such that $11\mid x+y$.

Published on 26 Mar 2026 - 4:36

score 445 · Answer 7 · 2021-04-05 22:27:25

445

Views

6 random integers from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$, at least one pair will have an odd sum.

Published on 05 Apr 2021 - 22:27

score 97 · Answer 8 · 2021-04-09 18:51:32

97

Views

Pigeonhole Principle Problem with $5$ people, can't be the case that there are $3$ strangers or $3$ acquaintances.

Published on 09 Apr 2021 - 18:51

score 61 · Answer 9 · 2021-04-10 14:00:21

61

Views

Hints for the following question

Published on 10 Apr 2021 - 14:00

score 89 · Answer 10 · 2026-03-28 03:03:03

89

Views

In an $8\times 8$ square, what's the min number of dots to be placed so that there's always a pair with distance apart at most $\sqrt8$?

Published on 28 Mar 2026 - 3:03

score 611 · Answer 11 · 2021-04-20 12:48:57

611

Views

Maximum "sum free" subset

Published on 20 Apr 2021 - 12:48

score 85 · Answer 12 · 2021-04-22 07:43:12

85

Views

Not sure how to connect the Pigeonhole principle to maximal clique size in finite graphs

Published on 22 Apr 2021 - 7:43

score 90 · Answer 13 · 2021-04-25 10:44:15

90

Views

Determining the number of maximum digits with coincidence restriction using Pigeonhole Principle

Published on 25 Apr 2021 - 10:44

score 535 · Answer 14 · 2021-04-27 22:55:50

535

Views

Using Pigeonhole Principle find two integers such that their difference equals an integer $j$

Published on 27 Apr 2021 - 22:55

score 102 · Answer 15 · 2021-04-30 18:37:23

102

Views

Proving same score given sum of score using PHP

Published on 30 Apr 2021 - 18:37

List Question

Prove that it in a regular 100-gon where each vertices is colored in one of 10 colors, there exists a rectangle colored in at most 2 colors.

Prove that if n + 1 distinct numbers are selected from 1 to 2n - 1, then there is always a number in selected ones that is sum of two other selected

Given a list of integers from $1$ to $1000$ inclusive, what is the smallest $k$ numbers you pick such that it has $3$ consecutive numbers?

If $X$ is a subset of $A$ with more than $n$ elements, then there exist $a,b \in X$ such that $ a \mid b $ or $b \mid a$.

Probability of birthday

Let $B\subset A = \{1,2,3,...,99,100\}$ and $|B|= 48$. Prove that exist $x,y\in B$, $x\ne y$ such that $11\mid x+y$.

6 random integers from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$, at least one pair will have an odd sum.

Pigeonhole Principle Problem with $5$ people, can't be the case that there are $3$ strangers or $3$ acquaintances.

Hints for the following question

In an $8\times 8$ square, what's the min number of dots to be placed so that there's always a pair with distance apart at most $\sqrt8$?

Maximum "sum free" subset

Not sure how to connect the Pigeonhole principle to maximal clique size in finite graphs

Determining the number of maximum digits with coincidence restriction using Pigeonhole Principle

Using Pigeonhole Principle find two integers such that their difference equals an integer $j$

Proving same score given sum of score using PHP

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