# May Make $\frac5{2020}$ 2020

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!

Using the good ol' functions like:

ceiling and exponential functions.

Here is a way with only just two digits!

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

• Might as well use $\lfloor\pi+\pi\rfloor$... – Daniel Mathias May 14 '20 at 1:25
• I'm not sure if using constant is allowed, as we can just have five $\pi$s divided by two thousand twenty $\pi$s. – athin May 14 '20 at 9:54
• 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! – JKHA May 15 '20 at 0:15
• @JKHA huh? 5 𝜋s divided by 2020 𝜋s by definition is equal to 5/2020. – Quintec May 15 '20 at 0:22
• @Quintec oh yeah, I should go to sleep, I was thinking of $\pi^5$, forget about that x) – JKHA May 15 '20 at 0:28

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

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, $$\frac{4}{1616}=\frac{5}{2020}$$

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

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

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

• I believe the actual symbol is $||$ (ex. $2||(3+4)=27$). – merrybot May 13 '20 at 18:16

This uses four digits as well:

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

where

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