Question

proof by letters with characters

score 58 · Answer 1 · 2026-04-12 08:33:15

58

Views

proof by letters with characters

Published on 12 Apr 2026 - 8:33

score 271 · Answer 2 · 2026-05-10 14:46:14

271

Views

Monochromatic triangle - graph coloring

Published on 10 May 2026 - 14:46

score 136 · Answer 3 · 2026-04-09 12:13:03

136

Views

Dealing with Pigeonhole Principle Problems

Published on 09 Apr 2026 - 12:13

score 177 · Answer 4 · 2026-04-10 06:05:36

177

Views

pigeon hole principle [arrangement]

Published on 10 Apr 2026 - 6:05

score 89 · Answer 5 · 2026-04-12 04:16:46

89

Views

Deducing divisibility based on Pigeonhole Principle

Published on 12 Apr 2026 - 4:16

score 239 · Answer 6 · 2026-04-16 21:02:30

239

Views

Show that the sum or difference of $a_i$ and $a_j$ from a set of seven distinct integers is divisible by 10

Published on 16 Apr 2026 - 21:02

score 1k · Answer 7 · 2026-04-12 07:19:26

1k

Views

Given 20 distinct positive integers, not greater than 70. Show that among their pairwise differences, at least four are equal.

Published on 12 Apr 2026 - 7:19

score 1.1k · Answer 8 · 2026-04-16 08:53:42

1.1k

Views

Given three permutations of $\{1,2,\dots,n^3+1\}$, prove two of them have a common subsequence of length $n+1$.

Published on 16 Apr 2026 - 8:53

score 1.5k · Answer 9 · 2026-04-16 12:29:35

1.5k

Views

Given any $n+2$ integers, show that there exist two of them whose sum, or else whose difference, is divisible by $2n$.

Published on 16 Apr 2026 - 12:29

score 53 · Answer 10 · 2026-04-09 03:58:13

53

Views

Pigeonhole Principle Problem - need help understanding the concept

Published on 09 Apr 2026 - 3:58

score 393 · Answer 11 · 2026-03-25 11:01:26

393

Views

Prove the geometric "Pigeonhole Principle"

Published on 25 Mar 2026 - 11:01

score 100 · Answer 12 · 2026-05-10 17:17:34

100

Views

Prove that there exists a set $Y$ such that for every $v$, there exists $y \in Y$ that is incident to $v$.

Published on 10 May 2026 - 17:17

score 158 · Answer 13 · 2026-04-13 16:53:17

Prove by using the Pigeonhole Principle that there are at least $5$ of the $41$ chess pieces on the $10×10$ board that are not on the same row.

score 5.2k · Answer 14 · 2026-04-13 13:08:24

5.2k

Views

A woman selects balls from a bowl at random …

Published on 13 Apr 2026 - 13:08

score 363 · Answer 15 · 2026-04-12 11:36:15

363

Views

105 integers contains a subsequence with sum divisible by 99.

Published on 12 Apr 2026 - 11:36

List Question

proof by letters with characters

Monochromatic triangle - graph coloring

Dealing with Pigeonhole Principle Problems

pigeon hole principle [arrangement]

Deducing divisibility based on Pigeonhole Principle

Show that the sum or difference of $a_i$ and $a_j$ from a set of seven distinct integers is divisible by 10

Given 20 distinct positive integers, not greater than 70. Show that among their pairwise differences, at least four are equal.

Given three permutations of $\{1,2,\dots,n^3+1\}$, prove two of them have a common subsequence of length $n+1$.

Given any $n+2$ integers, show that there exist two of them whose sum, or else whose difference, is divisible by $2n$.

Pigeonhole Principle Problem - need help understanding the concept

Prove the geometric "Pigeonhole Principle"

Prove that there exists a set $Y$ such that for every $v$, there exists $y \in Y$ that is incident to $v$.

Prove by using the Pigeonhole Principle that there are at least $5$ of the $41$ chess pieces on the $10×10$ board that are not on the same row.

A woman selects balls from a bowl at random …

105 integers contains a subsequence with sum divisible by 99.

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