## Four 4s

Another way to get 93 using an exponent of 0 is 4! x 4 - 4 - 4°

 Yo, I got 89!
 5 = (4x4+4)/4
 i wanted to get 1020 but i dont know how to do it.
 How about this: 1020=4^4x4-4
 hey thanks alot i really mean it too
 1 = 44/44 7 = 44//4-4 12=(44+4)/4 15=44/4+4 16=4+4+4+4 36=44-4-4 88=44+44
 1000 = 4^4*4-4! 10000 = (4!/4+4)^4 100000000 = (4!*4+4)^4
 I remember doing this at school! I do not recall being permitted to use .4 or %, though. But I seem to recall we were permitted to use '√' . 93 can also be got by this unintuitive term; 93=4![4-√√√[{√4}^-{4!}] Without %, 89 and 91 need both '√' and '.4' (though I like Joffe's, with the %) .
 in 1 post in the puzzles community on (nowadays inactive)orkut, i remember doing it. it involved the usage of double factorials too. ex 7!! = 1*3*5*7 = 105, 8!! = 2*4*6*8 = 384, etc i was able to find the solutions of all numbers from 1 to about 150 using the double factorial thing alongwith the usual operators like +,-,*,/,sqrt, and using the decimal point. if i find the solutions, i will post them here
 here are the answers - Code: 1 = 44/44 2 = (4/4) + (4/4) 3 = [(4*4) -4]/4 4 = (4/.4) - (4!/4) 5 = (4!/4) - (4/4) 6 = (4!/4)*(4/4) 7 = 4 + 4 - (4/4) 8 = 4 + 4 + 4 - 4 9 = 4 + 4 + (4/4) 10 = (44 - 4)/4 11 = (4/.4) + (4/4) 12 = (44 + 4)/4 13 = 4! - (44/4) 14 = (4/.4) + sqrt(4) + sqrt(4) 15 = (4*4) - (4/4) 16 = 4 + 4 + 4 + 4 17 = (4*4) + (4/4) 18 = (4/.4) + 4 + 4 19 = 4! - 4 - (4/4) 20 = (4! - 4) + 4 - 4 21 = 4! - 4 + (4/4) 22 = (44/4)*(sqrt(4)) 23 = 4! - sqrt(4) + (4/4) 24 = 44 + 4 - 4! 25 = 4! + sqrt(4) - (4/4) 26 = (4*4) + (4/.4) 27 = 4! + 4 - (4/4) 28 = 4! + 4 + 4 - 4 29 = 4! + 4 + (4/4) 30 = 4! + 4 + 4 - sqrt(4) 31 = 4! + 4 + 4 - sqrt(sqrt(sqrt(sqrt...sqrt(4)...))) 32 = (4^4)/(4+4) = 4^(4/(.4*4)) 33 = 4! + 4 + 4 + sqrt(sqrt(sqrt(sqrt...sqrt(4)...))) 34 = 4! + 4 + 4 + sqrt(4) 35 = 4! + (44/4) 36 = 44 - 4 - 4 37 = (4!/.4) - 4! + sqrt(sqrt(sqrt(sqrt...sqrt(4)...))) 38 = 44 - 4 - sqrt(4) 39 = 44 - 4 - sqrt(sqrt(sqrt(sqrt...sqrt(4)...))) 40 = (4!/.4) - 4! + 4 41 = 44 - 4 + sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 42 = 44 - 4 + sqrt(4) 43 = 44 - (4/4) 44 = 44 + 4 - 4 45 = 44 + (4/4) 46 = 44 + 4 - sqrt(4) 47 = 4! + 4! - (4/4) 48 = 4! + 4! + 4 - 4 49 = 4! + 4! + (4/4) 50 = 44 + 4 + sqrt(4) 51 = (4! - 4 + .4)/.4 52 = 44 + 4 + 4 53 = 4! + 4! + (sqrt(4)/.4) 54 = 4! + 4! + 4 + sqrt(4) 55 = (4!/.4) - (sqrt(4)/.4) 56 = 4! + 4! + 4 + 4 57 = (4! - sqrt(4))/.4 + sqrt(4) 58 = 4! + 4! + (4/.4) 59 = (4!/.4) - (4/4) 60 = (4!/.4) + 4 - 4 61 = (4!/.4) + (4/4) 62 = (4!/.4) + 4 - sqrt(4) 63 = ((4^4) - 4)/4 64 = 4^(4 - (4/4)) 65 = (4!/.4) + (sqrt(4)/.4) 66 = 44 + 4! - sqrt(4) 67 = (4! + sqrt(4))/.4 + sqrt(4) 68 = (4*4*4) + 4 69 = (4! + 4 - .4)/.4 70 = 44 + 4! + sqrt(4) 71 = (4! + 4.4)/.4 72 = 44 + 4! + 4 73 = 4! + 4! + 4! + sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 74 = 4! + 4! + 4! + 4 75 = (4! + 4 + sqrt(4))/.4 76 = 4! + 4! + 4! + 4 77 = ( 4 - sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) )^4 - 4 78 = (4! - 4)*4 - sqrt(4) 79 = (4! - sqrt(4))/.4 + 4! 80 = ((4*4) + 4)*4 81 = (4 - (4/4))^4 82 = (4! - 4)*4 + sqrt(4) 83 = (4! - .4)/.4 + 4! 84 = 44*(sqrt(4)) - 4 85 = ( 4 - sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) )^4 + 4 86 = 44*(sqrt(4)) - sqrt(4) 87 = 44*(sqrt(4)) - sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 88 = 44 + 44 89 = 44*(sqrt(4)) + sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 90 = 44*(sqrt(4)) + sqrt(4) 91 = (4!*4) - (sqrt(4)/.4) 92 = 44*(sqrt(4)) + 4 93 = (4!*4) - 4 + sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 94 = (4!*4) - 4 + sqrt(4) 95 = (4!*4) - (4/4) 96 = 4! + 4! + 4! + 4! 97 = (4!*4) - (4/4) 98 = (4!*4) + 4 - sqrt(4) 99 = (4!*4) + 4 - sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 100 = (4!*4) + sqrt(4) + sqrt(4)
 Code: 101 = (4!*4) + [sqrt(4)/.4] 102 = (4!*4) + 4 + sqrt(4) 103 = (4! + sqrt 4)*4 - sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 104 = (4!*4) + 4 + 4 105 = (4! + sqrt 4)*4 + sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 106 = (4! + sqrt 4)*4 + sqrt(4) 107 = (4 + (4!/4!!))!! + sqrt(4) double factorials introduced here 108 = (44/.4) - sqrt(4) 109 = (4 + (4!/4!!))!! + 4 110 = ((4!!)!! + 4!)/4 + 4!! 111 = (4! + 4)*4 - sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 112 = (44/.4) + sqrt(4) 113 = (4! + 4)*4 + sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 114 = (44/.4) + 4 115 = (sqrt(4)/.4)! - (sqrt(4)/.4) 116 = (4 + (4/4))! - 4 117 = (sqrt(4)/.4)! - 4 + sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 118 = (4 + (4/4))! - sqrt(4) 119 = (4 + (4/4))! - sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 120 = (4!/.4) + (4!/.4) = 120 121 = (4 + (4/4))! + sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 122 = (4 + (4/4))! + sqrt(4) 123 = (sqrt(4)/.4)! + 4 - sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 124 = (4 + (4/4))! + 4 125 = sqrt(sqrt(sqrt {[4 + (4/4)]^(4!)} )) 126 = [(4^4)/sqrt(4)] - sqrt(4) 127 = [(4^4)/sqrt(4)] - sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 128 = 4*4*(4+4) 129 = [(4^4)/sqrt(4)] + sqrt(sqrt(sqrt(sqrt...(sqrt(4))...))) 130 = [(4^4)/sqrt(4)] + sqrt(4) 131 = {[(4!!)!]/[(4!!)!!]} + 4! + sqrt(4) 132 = [(4^4)/sqrt(4)] + 4 133 = {[(4!!)!]/[(4!!)!!]} + 4! + 4 134 = (44/.4) + 4! 135 = (sqrt(4)/.4)! + (sqrt(4)/.4)!! 136 = [4! + (4/.4)]*4
 If both (specified base) logarithms and normal roots are permitted, then any n can be represented (actually with only 3 4's): $$n = -log_{4}(log_{4}(\overbrace{√√√...√√√}^{\text{2n of these}}(4)))$$ Or, to use the extra 4: $$n = -log_{4}(log_{4}(\overbrace{√√√...√√√}^{\text{2n+1 of these}}(4*4)))$$ Thanks for playing.
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