Question

7 fishermen caught exactly 100 fish and no two had caught the same number of fish. Then there are three who have together captured at least 50 fish.

score 12.3k · Answer 1 · 2026-03-25 13:34:19

12.3k

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7 fishermen caught exactly 100 fish and no two had caught the same number of fish. Then there are three who have together captured at least 50 fish.

Published on 25 Mar 2026 - 13:34

score 89 · Answer 2 · 2026-04-11 06:09:55

89

Views

How to show that $\dfrac{n^3 + 2n}{3}$ is an integer

Published on 11 Apr 2026 - 6:09

score 163 · Answer 3 · 2026-04-02 18:42:44

163

Views

What is $\sigma^2$ of the following permutation, $\sigma=31654287$.

Published on 02 Apr 2026 - 18:42

score 197 · Answer 4 · 2026-03-28 06:00:32

197

Views

In how many ways can I select 4 groups from 10 indistinguishable items where each selected group only contains either 0 or an odd number of items

Published on 28 Mar 2026 - 6:00

score 1.3k · Answer 5 · 2026-03-28 17:41:19

1.3k

Views

Showing that if n is a natural number larger than 3, then $n!>2^n$

Published on 28 Mar 2026 - 17:41

score 1.1k · Answer 6 · 2026-03-28 17:41:18

1.1k

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Prove by induction that, for all positive integers n, the following inequality holds:

Published on 28 Mar 2026 - 17:41

score 133 · Answer 7 · 2026-04-11 09:05:13

133

Views

Predicate Logic Negating a WFF, do signs cancel?

Published on 11 Apr 2026 - 9:05

score 420 · Answer 8 · 2026-03-28 06:00:04

420

Views

how many ways are there to divide 180 items into 36 groups of 5?

Published on 28 Mar 2026 - 6:00

score 128 · Answer 9 · 2026-04-10 21:38:16

128

Views

A strange inductive proof: Induction on $n$, for all positive integers $n,n\ge1$

Published on 10 Apr 2026 - 21:38

score 573 · Answer 10 · 2026-03-25 05:01:31

573

Views

Solution verification: showing $xRy$ on $\Bbb Z$ iff $3x-7y$ is even is an equivalence relation

Published on 25 Mar 2026 - 5:01

score 146 · Answer 11 · 2026-03-28 17:41:53

146

Views

By induction showing that $m^3\le2^m$ for $m\ge10$

Published on 28 Mar 2026 - 17:41

score 94 · Answer 12 · 2026-03-31 18:47:30

94

Views

prove if and only if logic equivalent to ($P\lor Q) \rightarrow (P\land Q $)(using the laws without truth table)

Published on 31 Mar 2026 - 18:47

score 46 · Answer 13 · 2026-04-10 09:48:20

46

Views

Solution of a system of congruence equations

Published on 10 Apr 2026 - 9:48

score 95 · Answer 14 · 2018-10-01 09:17:20

95

Views

Prove that $r_1s_1, r_2s_2, ..., r_{p-1}s_{p-1}$ is not a reduced residue system modulo p.

Published on 01 Oct 2018 - 9:17

score 223 · Answer 15 · 2026-04-11 08:20:43

223

Views

Proof that $n$ is a positive odd integer if $5n + 6$ is odd

Published on 11 Apr 2026 - 8:20

List Question

7 fishermen caught exactly 100 fish and no two had caught the same number of fish. Then there are three who have together captured at least 50 fish.

How to show that $\dfrac{n^3 + 2n}{3}$ is an integer

What is $\sigma^2$ of the following permutation, $\sigma=31654287$.

In how many ways can I select 4 groups from 10 indistinguishable items where each selected group only contains either 0 or an odd number of items

Showing that if n is a natural number larger than 3, then $n!>2^n$

Prove by induction that, for all positive integers n, the following inequality holds:

Predicate Logic Negating a WFF, do signs cancel?

how many ways are there to divide 180 items into 36 groups of 5?

A strange inductive proof: Induction on $n$, for all positive integers $n,n\ge1$

Solution verification: showing $xRy$ on $\Bbb Z$ iff $3x-7y$ is even is an equivalence relation

By induction showing that $m^3\le2^m$ for $m\ge10$

prove if and only if logic equivalent to ($P\lor Q) \rightarrow (P\land Q $)(using the laws without truth table)

Solution of a system of congruence equations

Prove that $r_1s_1, r_2s_2, ..., r_{p-1}s_{p-1}$ is not a reduced residue system modulo p.

Proof that $n$ is a positive odd integer if $5n + 6$ is odd

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