Make the numbers 1-50 using 2, 0, 2, 0

Make the numbers 1-50 using 2 0 2 0 in the given order. Use all four digits exactly once.

Allowed operations: +, -, x, /, ! (factorial), double factorial, exponentiation, square root, parentheses. Grouping (e.g. "20") is also allowed, as are decimals (e.g. ".2").

• Is squaring also a valid operation? What is the scoring mechanism to determine the "best" answer? – Avi Jan 3 at 21:32
• Squaring is not a valid operation. – Andrej Jakobčič Jan 3 at 21:44
• Can you group the like this: 0! grouped with 2 makes 12? – Duck Jan 3 at 22:25
• @Duck, no grouping like this! – Andrej Jakobčič Jan 3 at 22:40
• If we allow other functions we can put: $\left \lfloor 20^{\sqrt{\sqrt{2}}} \right \rfloor - 0!$ or $-2+.0\bar{2}^{-0!}$ or $-\Gamma(2)+.0\bar{2}^{-0!}$. – Andrej Jakobčič Jan 9 at 14:37

1 Answer

Anyone is welcome to edit and improve this answer, so don't checkmark this answer.
Bolded numbers mean they need to be solved or are impossible.

1

$$(2+0-2)+0!$$

2

$$2+(0*2)+0$$

3

$$2+0!+(2*0)$$

4

$$2+0+2+0$$

5

$$2+0!+2+0$$

6

$$2+0!+2+0!$$

7

$$(2+(0!))*2)+0!$$

8

$$2*(0!+2+0!)$$

9

$$(2+0!)*(2+0!)$$

10

$$(20/2+0)$$

11

$$(20/2+0!)$$

12

$$(2+0!)!*2+0$$

13

$$((2+0!)!*2)+0!$$

14

$$20-((2+0!)!)$$

15

$$(2+0!)/.20$$

16

$$(2+0!)/.2+0!$$

17

$$20-2-0!$$

18

$$20-2+0$$

19

$$20-2+0!$$

20

$$20+2*0$$

21

$$2-0!+20$$

22

$$20+2+0$$

23

$$20+2+0!$$

24

$$(2+0+2+0)!$$

25

$$((2*0!)*2)!+0!$$

26

$$20+((2+0!)!)$$

27

$$(2+0!)^{(2+0!)}$$

28

$$((2+0!)!)!!-20$$

29

$$((2+0!)!/.2)-0!$$

30

$$((2+0!)!/.2)+0$$

31

$$((2+0!)!/.2)+0!$$

32

$$2^{((0!+2)!-0!)}$$

33

$$2^{((0!/.2))}+0!$$

34

35

$$(2+0!)!^2-0!$$

36

$$(2+0!)!^2+0$$

37

$$(2+0!)!^2+0!$$

38

$$2(-0!+20)$$

39

$$20*2-0!$$

40

$$20+20$$

41

$$(20*2)+0!$$

42

$$2*(0!+20)$$

43

44

45

$$((2+0!)!)!!-2-0!$$

46

$$((2+0!)!)!!-2+0$$

47

$$((2+0!)!)!!-2+0!$$

48

$$2*(0!+2+0!)!$$

49

$$((2+0!)!)!!+2-0!$$

50

$$((2+0!)!)!!+2+0$$

• I have a premonition that 50 is going to be impossible. Good on you for keeping at it, though: +1 – Avi Jan 3 at 21:55
• Not sure - it's pretty tough to get off of 2 and 0 as the only numbers, with ordering restrictions – Avi Jan 3 at 22:31
• @AndrejJakobčič Clever 27, nice! – Avi Jan 3 at 22:37
• If anyone is welcome to improve this answer, it's better to mark it community wiki. – Glorfindel Jan 4 at 8:29
• @Glorfindel I agree, since Avi and I did significant parts of this. – Don Thousand Jan 4 at 13:26