Use two 2's, two 1's and two 8's to make the number 2018

Question

This is another number formation question. You must use each of $2$, $1$ and $8$ exactly twice to make the number $2018$. The rules are

1. Allowed symbols: $+$, $-$, $\times$, $\div$, $($, $)$, $\sqrt{\quad}$, $!$. Arbitrary functions (such as the logarithm) are not allowed.
2. The ordering of the numbers are not important.
3. It is OK to use numbers as superscript (exponent or the power for the radical symbol).
4. Concatenation is allowed although using $(2+1)1$ to construct $31$ is not allowed.
5. Ceiling or flooring is not allowed. $211\div2=105.5$, not $105$ or $106$.

6. The use of decimal point or scientific notation is not allowed.

   For example, $$(2+8)\times(2+1)!\times\sqrt{1+8}=180$$ is a valid construction, although this is not a solution because it does not equal $2018$.

Edit (after slvrbld posted his answer): Try to make $2108$ and $8102$ as well if you can.

(And of course, the more ways the better).

Second Edit I am thinking whether I can make all 4-digit numbers composed of 2, 0, 1 and 8 (numbers beginning with 0 do not count). I have solutions for some but not all of them. Once I find solution for all of them or find a well defined subset for which I have solutions, I will update it and make it a formal challenge here.

Answer 1

A possible solution:

$ 1\times2 + 8!/(12+8) $

Edit: more obscure approach:

$\displaystyle\binom{8\times8}{1\times1\times2} + 2 = \binom{64}{2} + 2 = 2018$

Answer 2

For 8102:

$ 8112-8-2 $

For 2108:

$ 2118-8-2 $

Answer 3

To build up on slvrblds solution by using only the pure numbers (without concatenation):

$2018 = 2 + 8! / (2 \times (8 + 1 + 1))$

Edit: Got another one with a multifactorial (for obscurity reasons):

$2018 = 1 + 1 + 8! \times 2 \times 2 \div 8!!!$

Answer 4

First time here :)

$8! / (18+2) + 2*1$

Answer 5

Are we restricted to Equations?

Argument: you need some sort of method to perceive the final result.

The only negative aspect of this answer is that it is not universal. Blind people would not understand how to read the digit of the final printed number as zero (0). Mathematics can be used by the blind, Braille is their chief source of information.

The symbol for 0 (zero) in Braille is a 3 x 2 matrix of:

| 0 1 | | 1 1 | | 0 0 |

which doesn't hold up mathematically as in Braille, using the sequence would result in 2818

(see Braille symbols here: https://www.pharmabraille.com/pharmaceutical-braille/the-braille-alphabet/)

Nevertheless, zero (0) is the absence of any sort of number, so processing this information (even for blind people reading Braille) this can allow for an intuitive understanding of the second digit as the non-integer zero (0 = chaos, absence of comprehensive entity).

Graphical solution using:
http://uniqcode.com/typewriter/

Sequence: 2 1 2 8 1 8 Keypress: 2 back 1 back 2 back 8 1 8

Lateral Thinking? You could convert to binary I suppose and manipulate them in that manner. Also, converting numbers to unicode and tweaking them would be an exercise in lateral thinking..

Anyway, I'm not a mathematician but after watching the movie "Arrival" two days ago, I see that skills in linguistics can help decipher 'classical' problems with left-field (right-hemisphere) tactics ;)