Question

show that some pair of 8 points in the unit square will be at most $\sqrt{5}/4$ units apart

score 126 · Answer 1 · 2022-10-06 23:31:00

126

Views

show that some pair of 8 points in the unit square will be at most $\sqrt{5}/4$ units apart

Published on 06 Oct 2022 - 23:31

score 621 · Answer 2 · 2026-04-03 05:20:32

621

Views

Show that all the nonzero roots of $f(x)$ are roots of unity. (A theorem of Kronecker)

Published on 03 Apr 2026 - 5:20

score 50 · Answer 3 · 2022-10-16 00:06:11

50

Views

"Hyper-pigeonhole principle": size of tail-avoiding sequence families

Published on 16 Oct 2022 - 0:06

score 187 · Answer 4 · 2022-10-16 09:47:18

187

Views

Dividing 100 members into two groups.

Published on 16 Oct 2022 - 9:47

score 75 · Answer 5 · 2022-10-16 16:25:30

75

Views

show each $x_i\in\mathbb{Q}$ is rational

Published on 16 Oct 2022 - 16:25

score 160 · Answer 6 · 2026-03-26 04:49:35

160

Views

Does such an "extremely" equally distributed real, bounded sequence exist?

Published on 26 Mar 2026 - 4:49

score 118 · Answer 7 · 2022-10-29 17:17:16

118

Views

One hundred people each with either all white hair or all black hair are arbitrarily seated in four rooms

Published on 29 Oct 2022 - 17:17

score 153 · Answer 8 · 2022-10-30 05:20:29

153

Views

Find largest subset in which all differences are divisible by $8$

Published on 30 Oct 2022 - 5:20

score 130 · Answer 9 · 2022-10-30 21:47:36

130

Views

An application of the pigeonhole principle on a $7\times 7$ board

Published on 30 Oct 2022 - 21:47

score 48 · Answer 10 · 2022-11-05 12:18:12

48

Views

How to prove that the max distance between 5 points on a unit square perimeter is 0.75

Published on 05 Nov 2022 - 12:18

score 79 · Answer 11 · 2022-11-05 16:36:26

79

Views

Pigeon Hole principle problem about baseball and training

Published on 05 Nov 2022 - 16:36

score 40 · Answer 12 · 2022-11-07 13:40:50

40

Views

Largest permutation of subset of $[n]$ with the property that every element in the right half is near to ($<n/2$ from) every element in the left half

Published on 07 Nov 2022 - 13:40

score 272 · Answer 13 · 2026-03-28 14:19:35

272

Views

What is the maximum value of $\sum_{i=1}^{n} \vert \sigma(i) - i \vert, $ where $\ \sigma\ $ is a permutation of $\ [n]\ ?$

Published on 28 Mar 2026 - 14:19

score 176 · Answer 14 · 2022-11-11 18:43:55

176

Views

Pigeonhole principle with unique sequence

Published on 11 Nov 2022 - 18:43

score 1.1k · Answer 15 · 2022-11-12 09:03:45

1.1k

Views

Show that if 5 integers are selected from the first 8 positive integers, there must be a pair of these integers with a sum equal to 9. (Pigeonhole)

Published on 12 Nov 2022 - 9:03

List Question

show that some pair of 8 points in the unit square will be at most $\sqrt{5}/4$ units apart

Show that all the nonzero roots of $f(x)$ are roots of unity. (A theorem of Kronecker)

"Hyper-pigeonhole principle": size of tail-avoiding sequence families

Dividing 100 members into two groups.

show each $x_i\in\mathbb{Q}$ is rational

Does such an "extremely" equally distributed real, bounded sequence exist?

One hundred people each with either all white hair or all black hair are arbitrarily seated in four rooms

Find largest subset in which all differences are divisible by $8$

An application of the pigeonhole principle on a $7\times 7$ board

How to prove that the max distance between 5 points on a unit square perimeter is 0.75

Pigeon Hole principle problem about baseball and training

Largest permutation of subset of $[n]$ with the property that every element in the right half is near to ($<n/2$ from) every element in the left half

What is the maximum value of $\sum_{i=1}^{n} \vert \sigma(i) - i \vert, $ where $\ \sigma\ $ is a permutation of $\ [n]\ ?$

Pigeonhole principle with unique sequence

Show that if 5 integers are selected from the first 8 positive integers, there must be a pair of these integers with a sum equal to 9. (Pigeonhole)

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