Question

Given 5 arbitrary points in the plane from which no 3 are collinear, prove that you can always choose 3 that are vertices of obtuse triangle.

score 141 · Answer 1 · 2026-04-02 03:51:25

141

Views

Given 5 arbitrary points in the plane from which no 3 are collinear, prove that you can always choose 3 that are vertices of obtuse triangle.

Published on 02 Apr 2026 - 3:51

score 332 · Answer 2 · 2017-10-24 20:10:57

332

Views

Pigeon Hole Principle with 13 birds somewhere

Published on 24 Oct 2017 - 20:10

score 573 · Answer 3 · 2017-10-26 13:04:25

573

Views

cover all squares in a square grid by moving to adjacent squares

Published on 26 Oct 2017 - 13:04

score 680 · Answer 4 · 2017-10-26 13:25:58

680

Views

Given an array A of size n with elements from 1 to k and another Array B of size k with elements 1 to n. Show that they have a subarray of same sum.

Published on 26 Oct 2017 - 13:25

score 2.3k · Answer 5 · 2017-10-26 15:29:00

2.3k

Views

Prove that the set of odd natural numbers is infinite by the Pigeonhole Principle.

Published on 26 Oct 2017 - 15:29

score 351 · Answer 6 · 2026-03-26 10:58:16

351

Views

pigeonhole principle, for a chessboard problem.

Published on 26 Mar 2026 - 10:58

score 749 · Answer 7 · 2017-11-06 08:25:32

749

Views

A Pigeonhole-Principle from IMO Shortlist.

Published on 06 Nov 2017 - 8:25

score 316 · Answer 8 · 2017-11-06 15:25:19

316

Views

Show that infinitely many members of $1,11,111,1111,\dots$ are divisible by $2^{2017}+1$.

Published on 06 Nov 2017 - 15:25

score 85 · Answer 9 · 2017-11-06 17:22:28

85

Views

Prove that a rectangular box can be inscribed with all white vertices in the sphere

Published on 06 Nov 2017 - 17:22

score 446 · Answer 10 · 2017-11-07 05:06:55

446

Views

Prove that any set of $3n+1$ numbers taken from $\{1,2,...,4n\}$ contains three different numbers $a$, $b$, $c$ such that $a|b$ and $b|c$.

Published on 07 Nov 2017 - 5:06

score 122 · Answer 11 · 2017-11-09 10:59:41

122

Views

Using pigeonhole to prove/disprove a certain number of consecutive vists

Published on 09 Nov 2017 - 10:59

score 217 · Answer 12 · 2017-11-10 06:06:58

217

Views

Pigeon hole principle with a set of $50$ integers

Published on 10 Nov 2017 - 6:06

score 158 · Answer 13 · 2017-11-11 15:55:20

158

Views

A problem on pigeon hole principle

Published on 11 Nov 2017 - 15:55

score 116 · Answer 14 · 2017-11-13 21:32:01

116

Views

Functions, Pigeonhole Principle Help

Published on 13 Nov 2017 - 21:32

score 511 · Answer 15 · 2017-11-14 05:16:29

511

Views

Prove there are $2$ numbers in a set whose difference is a multiple of $9$?

Published on 14 Nov 2017 - 5:16

List Question

Given 5 arbitrary points in the plane from which no 3 are collinear, prove that you can always choose 3 that are vertices of obtuse triangle.

Pigeon Hole Principle with 13 birds somewhere

cover all squares in a square grid by moving to adjacent squares

Given an array A of size n with elements from 1 to k and another Array B of size k with elements 1 to n. Show that they have a subarray of same sum.

Prove that the set of odd natural numbers is infinite by the Pigeonhole Principle.

pigeonhole principle, for a chessboard problem.

A Pigeonhole-Principle from IMO Shortlist.

Show that infinitely many members of $1,11,111,1111,\dots$ are divisible by $2^{2017}+1$.

Prove that a rectangular box can be inscribed with all white vertices in the sphere

Prove that any set of $3n+1$ numbers taken from $\{1,2,...,4n\}$ contains three different numbers $a$, $b$, $c$ such that $a|b$ and $b|c$.

Using pigeonhole to prove/disprove a certain number of consecutive vists

Pigeon hole principle with a set of $50$ integers

A problem on pigeon hole principle

Functions, Pigeonhole Principle Help

Prove there are $2$ numbers in a set whose difference is a multiple of $9$?

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