Question

If $a+b+c+d=1$ then why is the maximum value of $(a+1)(b+1)(c+1)(d+1)$ is ${\left(\frac{5}{4}\right)}^4$?

score 271 · Answer 1 · 2015-06-29 16:02:33

271

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If $a+b+c+d=1$ then why is the maximum value of $(a+1)(b+1)(c+1)(d+1)$ is ${\left(\frac{5}{4}\right)}^4$?

Published on 29 Jun 2015 - 16:02

score 471 · Answer 2 · 2015-06-30 02:43:34

471

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What is the number of mappings?

Published on 30 Jun 2015 - 2:43

score 2.2k · Answer 3 · 2026-03-29 07:29:02

2.2k

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Students in a class, girls sitting with boys and boys sitting with girls

Published on 29 Mar 2026 - 7:29

score 7.2k · Answer 4 · 2015-06-30 09:05:34

7.2k

Views

$(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3=24xyz$?

Published on 30 Jun 2015 - 9:05

score 1.8k · Answer 5 · 2015-07-03 12:21:43

1.8k

Views

A question in interview for trinity college, Cambridge

Published on 03 Jul 2015 - 12:21

score 127 · Answer 6 · 2015-07-03 16:40:30

127

Views

Why count it this way?

Published on 03 Jul 2015 - 16:40

score 1.1k · Answer 7 · 2026-04-01 23:33:39

1.1k

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Finding the smaller number of two given the ratio between sum, difference and product

Published on 01 Apr 2026 - 23:33

score 58 · Answer 8 · 2015-07-04 23:05:28

58

Views

Solve for b and d

Published on 04 Jul 2015 - 23:05

score 42 · Answer 9 · 2026-04-03 04:07:16

42

Views

More detailed explanation of how $2N_{h-2}$ becomes $2^{h/2}$?

Published on 03 Apr 2026 - 4:07

score 45 · Answer 10 · 2015-07-06 14:36:55

45

Views

A question on the representation of all integers in terms of the sum of other interger cubes

Published on 06 Jul 2015 - 14:36

score 533 · Answer 11 · 2015-07-06 16:59:47

Let $n$ be a positive integer and $S$ the set of points $(x,y)$ in the plane, where $x$ and $y$ are non-negative integers such that $x + y < n$.

score 617 · Answer 12 · 2015-07-06 17:20:11

617

Views

Maths challenge problem: Why is the number of teams which require 4 substitutions 32?

Published on 06 Jul 2015 - 17:20

score 100 · Answer 13 · 2026-03-29 05:42:55

100

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How can I solve this recurrence problem?

Published on 29 Mar 2026 - 5:42

score 53 · Answer 14 · 2015-07-06 18:16:27

53

Views

For $n \geq 2$, find $\theta_n, \theta_n > 1$ s.t. $-\log(1-\frac{1}{n}) = \frac{1}{n} + \frac{\theta_n}{2n^2}$

Published on 06 Jul 2015 - 18:16

score 1.4k · Answer 15 · 2015-07-09 02:58:51

1.4k

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Diophantus' Lifespan

Published on 09 Jul 2015 - 2:58

List Question

If $a+b+c+d=1$ then why is the maximum value of $(a+1)(b+1)(c+1)(d+1)$ is ${\left(\frac{5}{4}\right)}^4$?

What is the number of mappings?

Students in a class, girls sitting with boys and boys sitting with girls

$(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3=24xyz$?

A question in interview for trinity college, Cambridge

Why count it this way?

Finding the smaller number of two given the ratio between sum, difference and product

Solve for b and d

More detailed explanation of how $2N_{h-2}$ becomes $2^{h/2}$?

A question on the representation of all integers in terms of the sum of other interger cubes

Let $n$ be a positive integer and $S$ the set of points $(x,y)$ in the plane, where $x$ and $y$ are non-negative integers such that $x + y < n$.

Maths challenge problem: Why is the number of teams which require 4 substitutions 32?

How can I solve this recurrence problem?

For $n \geq 2$, find $\theta_n, \theta_n > 1$ s.t. $-\log(1-\frac{1}{n}) = \frac{1}{n} + \frac{\theta_n}{2n^2}$

Diophantus' Lifespan

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