Question

Math olympiad question involving pigeonhole principle

score 210 · Answer 1 · 2022-04-16 14:53:07

210

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Math olympiad question involving pigeonhole principle

Published on 16 Apr 2022 - 14:53

score 355 · Answer 2 · 2022-04-16 22:46:27

355

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169 points are chosen at random inside an equilateral triangle of perimeter 300.

Published on 16 Apr 2022 - 22:46

score 55 · Answer 3 · 2022-04-20 21:33:11

55

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Prove that in any subset of $9$ elements of $C$, there are two elements whose product is $1240$.

Published on 20 Apr 2022 - 21:33

score 94 · Answer 4 · 2022-04-20 22:10:22

94

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Is this proof logically sound?

Published on 20 Apr 2022 - 22:10

score 62 · Answer 5 · 2026-03-29 06:47:37

62

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Given irrational numbers $0<\gamma_1<\gamma_2<1,$ real numbers $0\leq a<b\leq 1,$ does $\exists n$ such that $\{n\gamma_1\}, \{n\gamma_2\}\in(a,b)?$

Published on 29 Mar 2026 - 6:47

score 530 · Answer 6 · 2022-05-01 17:02:36

530

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At any given point in time two players have finished the same number of games

Published on 01 May 2022 - 17:02

score 149 · Answer 7 · 2022-05-02 17:13:49

149

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Pigeonhole theorem

Published on 02 May 2022 - 17:13

score 132 · Answer 8 · 2026-03-25 23:39:26

132

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Formal application of Pigeonhole principle on voting and candidates

Published on 25 Mar 2026 - 23:39

score 43 · Answer 9 · 2022-05-12 13:59:20

43

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There are $n$ points inside a $1\times1$ square that can form a convex polygon. Can $3$ of them exist, such that $\mathcal{A}\le\frac{8}{n^2}$?

Published on 12 May 2022 - 13:59

score 139 · Answer 10 · 2022-05-15 07:18:07

139

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A beautiful problem on the Pigeonhole Principle

Published on 15 May 2022 - 7:18

score 140 · Answer 11 · 2022-05-15 13:59:46

140

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Prove that there is a circle containing exactly $2018$ points

Published on 15 May 2022 - 13:59

score 65 · Answer 12 · 2022-05-18 21:54:53

65

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In a group of 97 students, those who know the same amount of people are placed in the same group, smallest number of students in the largest group?

Published on 18 May 2022 - 21:54

score 1k · Answer 13 · 2022-05-22 19:03:19

1k

Views

Existence Problem of pigeonhole, selecting among a set of 50 numbers.

Published on 22 May 2022 - 19:03

score 125 · Answer 14 · 2022-05-26 09:47:18

125

Views

Explanation about solution for selecting $5$ out of $8$ integers and a pair adds to $9$

Published on 26 May 2022 - 9:47

score 351 · Answer 15 · 2022-05-27 10:11:37

351

Views

Circular table with $25$ boys and $25$ girls and someone always sitting among $2$ boys

Published on 27 May 2022 - 10:11

List Question

Math olympiad question involving pigeonhole principle

169 points are chosen at random inside an equilateral triangle of perimeter 300.

Prove that in any subset of $9$ elements of $C$, there are two elements whose product is $1240$.

Is this proof logically sound?

Given irrational numbers $0<\gamma_1<\gamma_2<1,$ real numbers $0\leq a<b\leq 1,$ does $\exists n$ such that $\{n\gamma_1\}, \{n\gamma_2\}\in(a,b)?$

At any given point in time two players have finished the same number of games

Pigeonhole theorem

Formal application of Pigeonhole principle on voting and candidates

There are $n$ points inside a $1\times1$ square that can form a convex polygon. Can $3$ of them exist, such that $\mathcal{A}\le\frac{8}{n^2}$?

A beautiful problem on the Pigeonhole Principle

Prove that there is a circle containing exactly $2018$ points

In a group of 97 students, those who know the same amount of people are placed in the same group, smallest number of students in the largest group?

Existence Problem of pigeonhole, selecting among a set of 50 numbers.

Explanation about solution for selecting $5$ out of $8$ integers and a pair adds to $9$

Circular table with $25$ boys and $25$ girls and someone always sitting among $2$ boys

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