5
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For May 2020, try to create $\dfrac{5}{2020}$ using the least possible number of integers in the set $\{1,3,4,6,7,8,9\}$.

$2$, $5$ and $0$ are not allowed.

Example:

$$\dfrac{4+1}{3\left(673+\frac13\right)}$$

Uses $1,1,3,3,3,4,6$ and $7$ $\implies$ $8$ numbers. You must do better than $7$ numbers.

You are allowed to use any operation as long as you can find a wikipedia page created before 2020, that's why there is a lateral thinking tag.

Improving puzzle - thanks to @athin's answer and @Daniel Mathias' comments Any mathematical constant apart from $\{1,3,4,6,7,8,9\}$ is not allowed!

$$\dfrac{\lfloor \phi \rfloor}{\lceil e^{\lfloor \pi + \pi\rfloor}\rceil} $$

is equal to $\frac{5}{2020}$ but it's not a valid solution!

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0
8
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Using the good ol' functions like:

ceiling and exponential functions.

Here is a way with only just two digits!

$$\frac{1}{\lceil \exp(6) \rceil} = \frac{1}{404} = \frac{5}{2020}$$

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    $\begingroup$ Might as well use $\lfloor\pi+\pi\rfloor$... $\endgroup$ – Daniel Mathias May 14 '20 at 1:25
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    $\begingroup$ I'm not sure if using constant is allowed, as we can just have five $\pi$s divided by two thousand twenty $\pi$s. $\endgroup$ – athin May 14 '20 at 9:54
  • $\begingroup$ 5 $\pi$s divided by 2020 $\pi$s is not equal to $5$ divided by $2020$ but the spirit of your comment is true! I'm editing my question accordingly to your answer and remark! $\endgroup$ – JKHA May 15 '20 at 0:15
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    $\begingroup$ @JKHA huh? 5 𝜋s divided by 2020 𝜋s by definition is equal to 5/2020. $\endgroup$ – Quintec May 15 '20 at 0:22
  • $\begingroup$ @Quintec oh yeah, I should go to sleep, I was thinking of $\pi^5$, forget about that x) $\endgroup$ – JKHA May 15 '20 at 0:28
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Here is a way to do it with four digits

$$\frac{5}{2020} = \frac{1}{8!! + 4! - 4} $$ where we have used double factorial

Here is a way to do it with three digits

$$ \frac{5}{2020} = \frac{1}{8!! + \sigma(\sigma(8))} $$ where $\sigma$ is the Divisor sum function

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Improved solution:

See Home prime.
$\frac{1}{93+HP(9)}=\frac{1}{93+311}=\frac{1}{404}=\frac{5}{2020}$

Straightforward solution:

Using five digits, $\frac{4}{1616}=\frac{5}{2020}$

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    $\begingroup$ Nice ;) Straightforward and optimal? $\endgroup$ – JKHA May 13 '20 at 12:50
  • $\begingroup$ @JKHA Likely optimal. Though I wouldn't call it yet. Could be a creative solution with fewer digits. $\endgroup$ – Daniel Mathias May 13 '20 at 12:53
  • $\begingroup$ I was asking you knowing there is better ;) $\endgroup$ – JKHA May 13 '20 at 13:16
  • $\begingroup$ @JKHA See improved solution. $\endgroup$ – Daniel Mathias May 13 '20 at 13:19
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    $\begingroup$ By the way, I like your straightforward solution a lot for its simplicity! $\endgroup$ – JKHA May 15 '20 at 0:39
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Using

string concatenation (here denoted by $\otimes$, e.g. $2\otimes5=25$), Wikipedia page about it was created in 2002 and even last modified in 2019

we can get

$$\frac1{4\otimes(6-6) \otimes 4}=\frac1{404}=\frac5{2020}$$.

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    $\begingroup$ I believe the actual symbol is $||$ (ex. $2||(3+4)=27$). $\endgroup$ – merrybot May 13 '20 at 18:16
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This uses four digits as well:

$$\frac{1}{4 \cdot p(13)}$$

where

$p(n)$ is the number of distinct integer partitions of $n$.

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