Question

Lets play some game!
Create integers starting from 1 using exactly four of 4. You may use some standard math notaton : plus,minus, square root, factorial , multiplication, division.
You can only proceed to work with the number \(n\) if you (or someone else) already did the \(n-1\).

Answer 1

Let me start:
\(1=4-4+\frac{4}{4}\)

Answer 2

\[(\log_{4} 4)^{4^{4}}\]

Answer 3

Thanks Daniel, please mention what the number is equal to :D

Answer 4

Lol, I did 1 again:
\[2= 4/4 + 4/4\]

Answer 5

\(3=\frac{4+4+4}{4}\)

Answer 6

\[4=4\cdot 4^{4-4}\]

Answer 7

\(5=4+4^{4-4}\)
\(6=4+\frac{4+4}{4}\)
\(7=(4\cdot \sqrt{4})-\frac{4}{4}\)

Answer 8

\[8 = \sqrt{4}*\sqrt[4]{4^4}\]

Answer 9

\(9=4+4+\frac{4}{4}\)

Answer 10

\[10 = \sqrt{4*4*4}+\sqrt{4}\]

Answer 11

\[11=\frac{4!}{\sqrt{4}}-\frac{4}{4}\]
\[12=4+4+\sqrt{4}+\sqrt{4}\]
\[13=\frac{4!}{\sqrt{4}}+\frac{4}{4}\]

Answer 12

\[14 = 4!*\sqrt{4}/4 + \sqrt{4}\]

Answer 13

\(15=\frac{44}{4}+4\)

Answer 14

16=4*4*4/4

Answer 15

17=(4*4)+(4/4)

Answer 16

\[18 + \sqrt{4}*\sqrt{4}*4 + \sqrt{4}\]

Answer 17

\[19 = 4! - 4 - 4/4\]

Answer 18

\[20 = 4*(4+\log_{4}4) \]

Answer 19

\(21=4!-4+\frac{4}{4}\)

Answer 20

4!/4*4-\[\sqrt{4}\]

Answer 21

Let me rewrite metarock result
\(22=\frac{4!}{4}\cdot 4-\sqrt{4}\)

Answer 22

\[23=4!-\sqrt{4} + 4/4\]

Answer 23

24=4*4 + 4 + 4

Answer 24

\[24 = 4*(4*\sqrt{4}-\sqrt{4})\]

Answer 25

\[25 = 4! + \sqrt{4}-4/4\]

Answer 26

\[25=4!+\frac{\sqrt{4\cdot 4}}{4}\]

Answer 27

\[26=4!+\frac{4+4}{4}\]

Answer 28

\[27=4!+4-\frac{4}{4}\]

Answer 29

28=4!*4/4 + 4

Answer 30

\(29=4!+4+\frac{4}{4}\)

Answer 31

\[30=4!+4+\sqrt{4}\]

Answer 32

Need to use four of 4 metarock!

Answer 33

sorry

Answer 34

30\[30=4!+\sqrt{4}+\sqrt{4}+\sqrt{4}\]

Answer 35

watchmath if i want to chat with u should i open the group chat below?

Answer 36

sure

Answer 37

\[31=(\sqrt{\sqrt{\sqrt{4^{4!}}}}/-\sqrt{4} )/\sqrt{4}\]

Answer 38

too good
probably this is the toughest one

Answer 39

\(32=4\cdot 4 + 4\cdot 4\)
\(33=(\sqrt{\sqrt{\sqrt{4^{4!}}}}+\sqrt{4})/\sqrt{4}\)

Answer 40

\(34=\left (\sqrt{\sqrt{\sqrt{4^{4!}}}} \right )/\sqrt{4}+\sqrt{4}\)

Answer 41

combinations of this can flit an 320 GB pc memory :P

Answer 42

You want to continue to play?
Try 35

Answer 43

:P ok i try

Answer 44

Ah maybe I don't know 35 either :(

Answer 45

I know it :D

Answer 46

\[\sum_{4}^{8}n \] mybe try this xd

Answer 47

But you can't use 8 :)

Answer 48

wathcmath how old are you?

Answer 49

very old so don't ask :D :D

Answer 50

4+4 =8
i tihnk i can use xd

Answer 51

just say xd

Answer 52

Ok, but then you run out of your 4

Answer 53

no :( there are 4 fours ^^

Answer 54

and I am 14 years old ^^or we can say 13,9911

Answer 55

13,8911*

Answer 56

How's life in Turkey?

Answer 57

really nice :) i am happy in there ^^

Answer 58

ad nd i lreally liked that site :) i learned limit and multiply today ^^ with the help of this site ^^

Answer 59

you can visit my site too and tell me what you think
http://ask.watchmath.com

Answer 60

okay but how old are you ?

Answer 61

:D :D

Answer 62

Ok, maybe you see this as cheating, but I wrote a short python script (46lines) that does find these things with at most 4 4's. I limited it to intermediate results of 100 so I got none for 33. But for 31 there's a nicer one: \[31 = 4! + \frac{4!+4}{4}\]

Answer 63

wow! that's good nowhereman
I wish I can do programming.

Answer 64

WIOW!

Answer 65

I want to learn programming, is python a good way to start?

Answer 66

It's easy to use and has many advances features, but I think for the beginner it is not strict enough. For example you have very loose typing of variables. On the other hand the syntax is really nice.
I'll just append the script, if you want to have a look :-)

Answer 67

Are you doing your diplom right now nowhereman? typically how long does it takes?

Answer 68

Here in germany, it normally takes 9 semester. But I'm one of the last ones to do a diplom. Now they all do bachelors/masters which take 6+4 semester mostly.

Answer 69

Then how much longer to get a doctorate?
It seems you are interested in functional analysis :)

Answer 70

Anything up from 2 years I guess; but I'm not completely sure if I want to go that path yet :-)

Answer 71

How many more years for you to finish your diplom?