Question

Does there exist a bijection that is not eventually equal to the identity, but has a finite number of "crosses"?

score 255 · Answer 1 · 2020-10-28 11:37:09

255

Views

Does there exist a bijection that is not eventually equal to the identity, but has a finite number of "crosses"?

Published on 28 Oct 2020 - 11:37

score 138 · Answer 2 · 2020-10-29 06:13:01

138

Views

Pigeon Hole Principle - 14 days, 10 physical exercises. How will you do PE on consecutive days at least once in the next fortnight.?

Published on 29 Oct 2020 - 6:13

score 398 · Answer 3 · 2020-10-29 14:01:03

398

Views

Prove a sequence consists a subsequence of consecutive terms whose product is a perfect square

Published on 29 Oct 2020 - 14:01

score 170 · Answer 4 · 2020-10-31 11:11:14

170

Views

How to prove that $n|(a-b)$, such that $a,b \in S$ and pick any $n + 1$ numbers from set $S$ using divisibility and Pigeonhole principle?

Published on 31 Oct 2020 - 11:11

score 61 · Answer 5 · 2020-11-03 03:24:47

61

Views

Count a subset of a finite set

Published on 03 Nov 2020 - 3:24

score 365 · Answer 6 · 2020-11-09 20:19:56

365

Views

Show that $(a − b)(b − c)(a − c)$ is always an even integer if $a, b,$ and $c$ are integers.

Published on 09 Nov 2020 - 20:19

score 76 · Answer 7 · 2020-11-11 16:54:40

76

Views

Pigeon hole principle to prove $a-b=9$ in subset.

Published on 11 Nov 2020 - 16:54

score 190 · Answer 8 · 2020-11-15 04:08:11

190

Views

Counting Problem: Pigeonhole principle

Published on 15 Nov 2020 - 4:08

score 47 · Answer 9 · 2020-11-15 09:29:03

47

Views

A graph with $100$ vertices

Published on 15 Nov 2020 - 9:29

score 154 · Answer 10 · 2020-11-20 02:41:50

154

Views

Counting problem concerning Generalized Pigeonhole Principle

Published on 20 Nov 2020 - 2:41

score 407 · Answer 11 · 2020-11-20 04:58:24

407

Views

Let A be a subset of {1, 2, 3 ... 2n-1, 2n} containing n + 1 elements. (Full Question below)

Published on 20 Nov 2020 - 4:58

score 366 · Answer 12 · 2020-11-22 20:07:33

Showing that in a given set of 7 distinct integers that there must be at least one pair in the set whose sum or difference is a multiple of 10.

score 79 · Answer 13 · 2020-11-24 04:18:57

79

Views

Prove that any set of 27 six-digit positive integers must have three subsets with the same sum.

Published on 24 Nov 2020 - 4:18

score 34 · Answer 14 · 2026-03-25 23:24:23

34

Views

Convergence/divergence of sum of finite products of functions of reciprocals of natural numbers

Published on 25 Mar 2026 - 23:24

score 80 · Answer 15 · 2020-11-29 14:46:13

80

Views

Prove the machine can make exactly $( 2x - y )$ cakes at a period of consecutive hours

Published on 29 Nov 2020 - 14:46

List Question

Does there exist a bijection that is not eventually equal to the identity, but has a finite number of "crosses"?

Pigeon Hole Principle - 14 days, 10 physical exercises. How will you do PE on consecutive days at least once in the next fortnight.?

Prove a sequence consists a subsequence of consecutive terms whose product is a perfect square

How to prove that $n|(a-b)$, such that $a,b \in S$ and pick any $n + 1$ numbers from set $S$ using divisibility and Pigeonhole principle?

Count a subset of a finite set

Show that $(a − b)(b − c)(a − c)$ is always an even integer if $a, b,$ and $c$ are integers.

Pigeon hole principle to prove $a-b=9$ in subset.

Counting Problem: Pigeonhole principle

A graph with $100$ vertices

Counting problem concerning Generalized Pigeonhole Principle

Let A be a subset of {1, 2, 3 ... 2n-1, 2n} containing n + 1 elements. (Full Question below)

Showing that in a given set of 7 distinct integers that there must be at least one pair in the set whose sum or difference is a multiple of 10.

Prove that any set of 27 six-digit positive integers must have three subsets with the same sum.

Convergence/divergence of sum of finite products of functions of reciprocals of natural numbers

Prove the machine can make exactly $( 2x - y )$ cakes at a period of consecutive hours

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