[Guest]

This may have been posted before.

How high can you count using four fours. You can use all mathematical symbols etc. and concatenate the 4's e.g. 4444. here's a start,

44/44 =1

4/4 + 4/4 =2

(4+4+4)/4 =3

There is a record for the highest number achieved somewhere, I'm sure one of you will know where.

[plainglazed]

arcsin of 1/2 yields pi/6, not 30.

((4-4/4)!)!/4!

that's a matter of degrees...But yours is better for sure

Edited October 14, 2009 by plainglazed

[Guest]

I'll give a hint at this stage that will assist in future numbers. It is allowable to use 0.4 in the calculations. The 0 can be omitted and the decimal point can be used as an operator just as the sqrt can be used without using a 2.

[Guest]

by 4 conjunct 4, I mean 4 and 4 make 44

so...

(4! conjunct 4)/4 - 4!

[Guest]

With the decimal point:

33 = sqrt4/(.4) + 4! + 4

34 = 4! + 4 + 4 + sqrt4

35 = 4! + (4!-sqrt4)/sqrt4

36 = 4! + 4 + 4 + 4

37 = 4! + (4!+sqrt4)/sqrt4

38 = 44 - 4 - sqrt4

39 = 44 - sqrt4/(.4)

40 = sqrt(4^4) * sqrt4/(.4)

41 = 4! + 4! - sqrt4/(.4)

42 = 44 - 4 + sqrt4

43 = 44 - (4/4)

44 = 44 - 4 + 4

45 = 44 + (4/4)

46 = 44 + 4 - sqrt4

[Guest]

Well since the OP hasn't discredited sqrt or permutations/combinations, I can get up to 30. I'm stuck on 31.

nobody - could you check your 30?

thanks ljb, I made a simple notation error, sorry.

4!+(4-4/4)!=30

if sqrt is valid then

(OP has confirmed that .4 is valid and equal to 0.4)

(4!/√4 + .4)/.4=31

otherwise I'm also stuck on 31.

I'll wait for OP to confirm sqrt before work further.

Edited October 15, 2009 by nobody

[Guest]

thanks ljb, I made a simple notation error, sorry.

4!+(4-4/4)!=30

if sqrt is valid then

(OP has confirmed that .4 is valid and equal to 0.4)

(4!/√4 + .4)/.4=31

otherwise I'm also stuck on 31.

I'll wait for OP to confirm sqrt before work further.

Square root is valid. So is .4 Here is a safe 31. ((4+sqrt 4)!+4!)/4! = 31

[Guest]

from the point where psychic left:

47=4!+4!-4/4

48=4!+4!+4-4

49=4!+4!+4/4

50=4!+4!+4-√4

51=4!+4!+√(4/.4^-) -->(.4- =0.4444 = 4/9)

52=4!+4!+4/√4

53=44+4/.4^-

54=4!+4!+4!/4

55=4!/.4^- +4/4

56=4!+4!+4+4

57=4!+4!+4/.4^-

58=4!+4!+4/.4

Edited October 15, 2009 by nobody

[Guest]

from the point where psychic left:

47=4!+4!-4/4

48=4!+4!+4-4

49=4!+4!+4/4

50=4!+4!+4-√4

51=4!+4!+√(4/.4^-) -->(.4- =0.4444 = 4/9)

52=4!+4!+4/√4

53=44+4/.4^-

54=4!+4!+4!/4

55=4!/.4^- +4/4

56=4!+4!+4+4

57=4!+4!+4/.4^-

58=4!+4!+4/.4

Sorry to be a nitpick. I guess I'm confused by your notation - you're saying I can get 9 from 4/.4^- ? Could you please explain that notation?

EDIT: saw the explanation on 51, but still unsure of the validity

Edited October 15, 2009 by ljb

[Guest]

I got 51, 53, 55, and 57 without the 4^- notation. Also the math on 52 didn't look right.

(4! 4 + .4) / .4 = 51

44 + 4 + 4 = 52

((4! sqrt(4)) / .4) sqrt(2) = 53

(4! / .4) (sqrt(4) / .4) = 55

((4! sqrt(4)) / .4) + sqrt(2) = 57

(4! / .4) 4/4 = 59

(4^4)/4 4 = 60

(4! / .4) + 4/4 = 61

(4! / .4) + 4 sqrt(4) = 62

((4! + sqrt(4)) / .4) sqrt(2) = 63

4^(4! / (4+4)) = 64

(4! / .4) + (sqrt(4) / .4) = 65

(4! / .4) + 4 + sqrt(4) = 66

((4! + sqrt(4)) / .4) + sqrt(2) = 67

(4^4)/4 + 4 = 68

Edited October 15, 2009 by ljb

[Guest]

I'm stuck on 73... anyone care to help?

Sorry... seem to be having issues with the spoiler

(4! + 4 – .4) / .4 = 69

(4+4)! / (4! * 4!) = 70

(4! + 4 + .4) / .4 = 71

4! * 4! / (4 + 4) = 72

4! + 4! + 4! + sqrt(4) = 74

(4! + 4 + sqrt(4)) / .4 = 75

4 * (4! – (sqrt(4) / .4)) = 76

Edited October 15, 2009 by ljb

[Guest]

I'm stuck on 73 too. 71 took me a while, I had to work backwards to find the solution.

73 may not be possible.

[Guest]

I don't know why the "spoiler" won't work.

Here is 73. (4! C sqrt 4)/4 + 4 = 73 using nCr

[Guest]

Hint. There's one operator that hasn't been used yet that will be required ahead.

[Guest]

Hint. There's one operator that hasn't been used yet that will be required ahead.

Actually there's two operators that might prove useful.

Gamma (Г) , Г(n) = (n-1)!

~ Repeating i.e. 4/.4~ = 9

Edited October 15, 2009 by Forcedhand

[Guest]

Hint. There's one operator that hasn't been used yet that will be required ahead.

nPr fair game too?

[Guest]

nPr fair game too?

Yep, why not

[Guest]

(4 / .4~)^sqrt(4) – 4 = 77

(Γ(4) * (4 / .4~)) + 4! = 78

(4 / .4~)^sqrt(4) – sqrt(4) = 79

4 * 4! – 4 * 4 = 80

(4 - .4) / .4)^sqrt(4) = 81

(4! / .4) + 4! – sqrt(4) = 82

(4 / .4~)^sqrt(4) + sqrt(4) = 83

(Γ(4 + 4) / 4!) * .4 = 84

(4 / .4~)^sqrt(4) + 4 = 85

4 * 4! – (4 / .4) = 86

4 * 4! – (4 / .4~) = 87

44 + 44 = 88

[Guest]

44 * sqrt(4) + Γ(sqrt(4)) = 89

4 * 4! – 4 – sqrt(4) = 90

4 * 4! – (sqrt(4) / .4) = 91

4 * (4! – 4/4) = 92

4 * 4! – sqrt(4 / .4~) = 93

4 * 4! – 4 + sqrt(4) = 94

4 * 4! – 4/4 = 95

4 * 4! + 4 – 4 = 96

4 * 4! + 4/4 = 97

4 * 4! + 4 – sqrt(4) = 98

4 * 4! + sqrt(4 / .4~) = 99

(44 – 4) / .4 = 100

4 * 4! + (sqrt(4) / .4) = 101

4 * 4! + 4 + sqrt(4) = 102

4 * 4! + (4 / .4~) = 103

4 * 4! + 4 + 4 = 104

(44 – sqrt(4)) / .4 = 105

(44 / .4) – 4 = 106

[Guest]

44 * sqrt(4) + Γ(sqrt(4)) = 89

4 * 4! – 4 – sqrt(4) = 90

4 * 4! – (sqrt(4) / .4) = 91

4 * (4! – 4/4) = 92

4 * 4! – sqrt(4 / .4~) = 93

4 * 4! – 4 + sqrt(4) = 94

4 * 4! – 4/4 = 95

4 * 4! + 4 – 4 = 96

4 * 4! + 4/4 = 97

4 * 4! + 4 – sqrt(4) = 98

4 * 4! + sqrt(4 / .4~) = 99

(44 – 4) / .4 = 100

4 * 4! + (sqrt(4) / .4) = 101

4 * 4! + 4 + sqrt(4) = 102

4 * 4! + (4 / .4~) = 103

4 * 4! + 4 + 4 = 104

(44 – sqrt(4)) / .4 = 105

(44 / .4) – 4 = 106

103 incorrect; fixed below. need help on 107.

(4! + sqrt(4)) * 4 - Γ(sqrt(4)) = 103

(44 / .4) – sqrt(4) = 108

(44 – .4) / .4 = 109

(sqrt(4) / .4)! – (4 / .4) = 110

444 / 4 = 111

(44 / .4) + sqrt(4) = 112

(4! + 4) * 4 + Γ(sqrt(4)) = 113

(44 / .4) + 4 = 114

(44 + sqrt(4)) / .4 = 115

4 * (4! + (sqrt(4)/ .4)) = 116

(sqrt(4) / .4)! – sqrt(4 / .4~) = 117

(sqrt(4) / .4)! – 4 + sqrt(4) = 118

(sqrt(4) / .4)! – 4/4 = 119

(44 + 4) / .4 = 120

(sqrt(4) / .4)! + 4/4 = 121

(sqrt(4) / .4)! + 4 – sqrt(4) = 122

(sqrt(4) / .4)! + sqrt(4 / .4~) = 123

(4^4 / sqrt(4)) – 4 = 124

(sqrt(4) / .4)! + (sqrt(4) / .4) = 125

(sqrt(4) / .4)! + 4 + sqrt(4) = 126

(4^4 / sqrt(4)) – Γ(sqrt(4)) = 127

(4^4 / sqrt(4)) * Γ(sqrt(4)) = 128

(sqrt(4) / .4)! + (4 / .4~) = 129

(sqrt(4) / .4)! + (4 / .4) = 130

[Guest]

(4/4)con4 +4!

Can anybody get 39 without the use of sqrt? I banged my head against the wall for an hour and couldn't figure it out. I believe we've been able to solve everything up to 39 without sqrt, so I may have found the limit.

I wonder how high the limit with sqrt is... 130 already, sheesh

[Guest]

(4/4)con4 +4!

Can anybody get 39 without the use of sqrt? I banged my head against the wall for an hour and couldn't figure it out. I believe we've been able to solve everything up to 39 without sqrt, so I may have found the limit.

I wonder how high the limit with sqrt is... 130 already, sheesh

(4*4 - .4)/.4 = 39

[Guest]

4444!

if someone can come up with something bigger i'd like to see it.

(4444!)!

or if you wanna limit it to 1 factorial operator

(4^4^4^4)!

You said you wanted to see it

[Guest]

4!+4!/(4*.4)

(4/4)con4 +4!

Can anybody get 39 without the use of sqrt? I banged my head against the wall for an hour and couldn't figure it out. I believe we've been able to solve everything up to 39 without sqrt, so I may have found the limit.

I wonder how high the limit with sqrt is... 130 already, sheesh

[Guest]

Completely forgot about .4

-.-

[Guest]

need help on 107.

here is my approach for 107:

First I must explain my notation that I had used at my previous post:

I used 0.4^- as 0.444444444 and it's also equal to 4/9. Indeed - sign should be just over the "4"

I suppose this is a valid notation, but any objection will be accepted by me.

So:

107= 44/.4^- + 4 + 4

= 44/(4/9) + 4 + 4

= 44 * 9 /4 + 4 + 4

= 11 * 9 + 4 + 4

= 99 + 4 + 4