4 4's puzzle ?

Question

Alright, so here's how the game is played:

You're trying to make as many numbers as possible using 4 4's or less, in an attempt to try to prove an old theory: "You can make any whole number using only four instances of the number four and commonly used mathematical symbols."

So so far, the symbols allowed are:
1. All standard mathematical operators (+ - * /)
2. Factorials (4! = 4*3*2*1)
3. Square roots, arbitrary roots (the index is included in the 4 4's)
4. Repeat signs (denoted with an apostrophe ' or grave accent `, ex. 0.4` = 0.4444444.....)
5. Exponentiation (denoted with a caret ^, 4^4 = 4*4*4*4)
6. Decimals do not require a leading zero. So you could put .4 instead of 0.4.

I'll start:
0 = 4-4
1 = 4/4
2 = sqrt(4)
3 = 4 - 4/4
4 = 4
5 = 4 + 4/4
6 = 4 + sqrt(4)
7 = 4 + 4 - 4/4
8 = 4 + 4
9 = 4 + 4 + 4/4
10 = 4 + 4 + sqrt(4)

And the next person would continue from 11, 12, and so on, and introduce new symbols and explaining them if necessary.

Answer 1

Is this a question that you need help solving, or just a game you want other people to play in their spare time? In any case, here are the next few for you:

11 = (4! / sqrt(4) ) - 4/4
12 = (4 x 4) - 4
13 = (4! / sqrt(4) ) + 4/4
14 = (4 x 4) - sqrt(4)
15 = (4 x 4) - 4/4
16 = 4 x 4
17 = (4 x 4) + 4/4
18 = 4! - 4 - sqrt(4)
19 = 4! - 4 - 4/4
20 = 4! - 4
21 = 4! - (4 - 4/4)
22 = 4! - sqrt(4)
23 = 4! - 4/4
24 = 4!
25 = 4! + 4/4
26 = 4! + sqrt(2)
27 = 4! + (4 - 4/4)
28 = 4! + 4
29 = 4! + 4 + 4/4
30 = 4! + 4 + sqrt(4)

Answer 2

How far do you expect someone to go?
I have done 1 to 40 in the past without too many problems.
4! may be of use to you.
11 = (4! / 4) + (4 - 4)
Where 4! = 4.3.2.1 = 24
Could try others if you are stuck.
eg 12 = 4 + 4 + √4 + √4
eg 13 = (4! / √4) + (4 / 4)
eg 14 = 4 + 4 + 4 + √4
eg 15 = (4 x 4) - (4/4)
eg 17 = (4 x 4) + (4/4)
etc!

PS
Some of those answering are not using FOUR FOURS which is the whole point of the exercise!

Answer 3

i've got considered this questio before, even though it particularly is impossible with basically those symbols. it particularly is often finished like this: 4 divided by utilising 4 equals a million then plus 4 equals 5 then circumstances 4 equals 20

Answer 4

mmh, let us see if I get it

11 = 4!+sqrt(4)
12 = 4!-4
13 = 4!
14 = 4!+sqrt(4)
15 = 4*4
16 = 4*4-4
17 = 4^4
18 = 4^4+4
19 =4^4+4!
20 = 4!^4!^4!^4! <--huuuuge :)

Answer 5

Sorry no 11

12 - (4*4)-4