## watchmath 5 years ago 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 $$n-1$$.

1. watchmath

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

2. anonymous

$(\log_{4} 4)^{4^{4}}$

3. watchmath

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

4. anonymous

Lol, I did 1 again: $2= 4/4 + 4/4$

5. watchmath

$$3=\frac{4+4+4}{4}$$

6. watchmath

$4=4\cdot 4^{4-4}$

7. watchmath

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

8. anonymous

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

9. watchmath

$$9=4+4+\frac{4}{4}$$

10. anonymous

$10 = \sqrt{4*4*4}+\sqrt{4}$

11. watchmath

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

12. anonymous

$14 = 4!*\sqrt{4}/4 + \sqrt{4}$

13. watchmath

$$15=\frac{44}{4}+4$$

14. anonymous

16=4*4*4/4

15. anonymous

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

16. anonymous

$18 + \sqrt{4}*\sqrt{4}*4 + \sqrt{4}$

17. anonymous

$19 = 4! - 4 - 4/4$

18. anonymous

$20 = 4*(4+\log_{4}4)$

19. watchmath

$$21=4!-4+\frac{4}{4}$$

20. anonymous

4!/4*4-$\sqrt{4}$

21. watchmath

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

22. anonymous

$23=4!-\sqrt{4} + 4/4$

23. anonymous

24=4*4 + 4 + 4

24. anonymous

$24 = 4*(4*\sqrt{4}-\sqrt{4})$

25. anonymous

$25 = 4! + \sqrt{4}-4/4$

26. watchmath

$25=4!+\frac{\sqrt{4\cdot 4}}{4}$

27. watchmath

$26=4!+\frac{4+4}{4}$

28. watchmath

$27=4!+4-\frac{4}{4}$

29. anonymous

28=4!*4/4 + 4

30. watchmath

$$29=4!+4+\frac{4}{4}$$

31. anonymous

$30=4!+4+\sqrt{4}$

32. watchmath

Need to use four of 4 metarock!

33. anonymous

sorry

34. anonymous

30$30=4!+\sqrt{4}+\sqrt{4}+\sqrt{4}$

35. anonymous

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

36. watchmath

sure

37. watchmath

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

38. anonymous

too good probably this is the toughest one

39. watchmath

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

40. watchmath

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

41. anonymous

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

42. watchmath

You want to continue to play? Try 35

43. anonymous

:P ok i try

44. watchmath

Ah maybe I don't know 35 either :(

45. watchmath

I know it :D

46. anonymous

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

47. watchmath

But you can't use 8 :)

48. anonymous

wathcmath how old are you?

49. watchmath

very old so don't ask :D :D

50. anonymous

4+4 =8 i tihnk i can use xd

51. anonymous

just say xd

52. watchmath

Ok, but then you run out of your 4

53. anonymous

no :( there are 4 fours ^^

54. anonymous

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

55. anonymous

13,8911*

56. watchmath

How's life in Turkey?

57. anonymous

really nice :) i am happy in there ^^

58. anonymous

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

59. watchmath

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

60. anonymous

okay but how old are you ?

61. anonymous

:D :D

62. nowhereman

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: $31 = 4! + \frac{4!+4}{4}$

63. watchmath

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

64. anonymous

WIOW!

65. watchmath

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

66. nowhereman

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 :-)

67. watchmath

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

68. nowhereman

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.

69. watchmath

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

70. nowhereman

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

71. watchmath

How many more years for you to finish your diplom?