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Floor function: Maths Olympiad problem

score 702 · Answer 1 · 2026-02-23 11:59:32

702

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Floor function: Maths Olympiad problem

Published on 23 Feb 2026 - 11:59

score 1.2k · Answer 2 · 2016-08-24 13:13:54

1.2k

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One-sided limits for Greatest Integer Function evaluating to 0 / 0

Published on 24 Aug 2016 - 13:13

score 1.3k · Answer 3 · 2016-08-30 03:12:56

1.3k

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Can floor functions be used to "cycle" between values?

Published on 30 Aug 2016 - 3:12

score 4.3k · Answer 4 · 2016-09-01 03:19:32

4.3k

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limit of floor function, ceiling function and fractions

Published on 01 Sep 2016 - 3:19

score 140 · Answer 5 · 2016-09-04 19:48:39

140

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How to prove that : $\sum \limits_{k=0}^{n-1} \lfloor x+\frac{k}{n}\rfloor = \lfloor nx\rfloor$?

Published on 04 Sep 2016 - 19:48

score 159 · Answer 6 · 2016-09-05 12:46:38

159

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Transformation of r.v. with floor function

Published on 05 Sep 2016 - 12:46

score 86 · Answer 7 · 2016-09-06 12:11:36

86

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Connection between ceil and round

Published on 06 Sep 2016 - 12:11

score 116 · Answer 8 · 2016-09-07 07:15:37

116

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How to prove $\left\lceil\frac{x}y\right\rceil=\left\lfloor\frac{x-1}y\right\rfloor+1$ for positive integers $x,y$?

Published on 07 Sep 2016 - 7:15

score 319 · Answer 9 · 2016-09-07 08:07:17

319

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$\sum_{n=1}^{2016}\left\lfloor\frac{\sqrt n}{10}\right\rfloor$ in 2 minutes

Published on 07 Sep 2016 - 8:07

score 89 · Answer 10 · 2016-09-07 10:53:46

89

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$\left\lfloor x\right\rfloor + \left\lfloor n - x\right\rfloor = n -1$

Published on 07 Sep 2016 - 10:53

score 76 · Answer 11 · 2016-09-07 13:06:28

if $\left\lfloor x/2\right\rfloor$ is odd, show that $\left\lfloor \left\lfloor x/2\right\rfloor /2\right\rfloor = \left\lfloor x/4 \right\rfloor$

score 126 · Answer 12 · 2016-09-08 12:28:43

126

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Solving the equation: $ f ( n ) = \left \lfloor \frac n 2 \right \rfloor $

Published on 08 Sep 2016 - 12:28

score 260 · Answer 13 · 2016-09-09 04:34:47

260

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How to derive the following flooring function?

Published on 09 Sep 2016 - 4:34

score 2.6k · Answer 14 · 2016-09-09 21:30:02

2.6k

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Find all $x$ for which $\left| x - \left| x-1 \right| \right| = \lfloor x \rfloor$

Published on 09 Sep 2016 - 21:30

score 1k · Answer 15 · 2016-09-09 22:20:59

1k

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Prove that $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y \rfloor + \lfloor x+y \rfloor$ for all real $x$ and $y$.

Published on 09 Sep 2016 - 22:20

List Question

Floor function: Maths Olympiad problem

One-sided limits for Greatest Integer Function evaluating to 0 / 0

Can floor functions be used to "cycle" between values?

limit of floor function, ceiling function and fractions

How to prove that : $\sum \limits_{k=0}^{n-1} \lfloor x+\frac{k}{n}\rfloor = \lfloor nx\rfloor$?

Transformation of r.v. with floor function

Connection between ceil and round

How to prove $\left\lceil\frac{x}y\right\rceil=\left\lfloor\frac{x-1}y\right\rfloor+1$ for positive integers $x,y$?

$\sum_{n=1}^{2016}\left\lfloor\frac{\sqrt n}{10}\right\rfloor$ in 2 minutes

$\left\lfloor x\right\rfloor + \left\lfloor n - x\right\rfloor = n -1$

if $\left\lfloor x/2\right\rfloor$ is odd, show that $\left\lfloor \left\lfloor x/2\right\rfloor /2\right\rfloor = \left\lfloor x/4 \right\rfloor$

Solving the equation: $ f ( n ) = \left \lfloor \frac n 2 \right \rfloor $

How to derive the following flooring function?

Find all $x$ for which $\left| x - \left| x-1 \right| \right| = \lfloor x \rfloor$

Prove that $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y \rfloor + \lfloor x+y \rfloor$ for all real $x$ and $y$.

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