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The Four Fours challenge (math)

69 = (4?)? + 4? +sqrt4 + sqrt4 70 = 4! + 4! + 4! - sqrt4 71 = (4?)? + (sqrt4*sqrt4*4) 72 = (sqrt4+sqrt4)! + 4! + 4! 73 = 4! + (4?)? -4 - sqrt4 74 = 4! + 4! + 4! +sqrt4 75 = (4?)? + (4*4) + 4 76 = 4! + 4! + 4! + 4 77 = (4?+sqrt4)? - (4/4) 78 = (4 + 4 + sqrt4 + sqrt4)? 79 = (4? + sqrt4)? + (4/4) 80 = 4?*(4+sqrt4+sqrt4) 81 = (4?)? + 4! + (4/sqrt4) 82 = (4? + sqrt4)? + sqrt4 + sqrt4 83 = (4?)? + 4! +sqrt4 + sqrt4 84 = (4? + sqrt4)? + 4 + sqrt4 85 = (4?)? + 4? + 4? + 4? 86 = (4? + sqrt4)? + 4 + 4 87 = 4? + 4! + 4 + 4 88 = 4*4*4 + 4! 89 = (4?+4)? - 4*4 90 = (4+4)*(4?) + 4? 91 = (4?)? + (sqrt4+sqrt4+4)? 92 = 4! + (4? + sqrt4)? - 4? 93 = (4?)? + (4+4)? +sqrt4 94 = (4? + sqrt4)? + (4*4) 95 = (4? + sqrt4 + sqrt4) - 4? 96 = (sqrt4 + sqrt4)!*(sqrt4+sqrt4) 97 = (4? + 4)? - 4 - 4 98 = (4? + sqrt4)? +4? + 4? 99 = (4? + sqrt4)? + (4+sqrt4)? 100 = ((4+sqrt4)? + 4)*4 Phew.

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Posted: 8/23/2005 9:37 PM

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Dacicus

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73 = ((√4)?) ^ 4 - 4 - 4 74 = (4 + √4)? × 4 - 4? 75 = (4?) × (4?) × (√4)? / 4 76 = ((√4)?) ^ 4 - √4 - (√4)? 77 = ((√4)?) ^ 4 - √4 - √4 78 = (√4)? × (√4)? ^ (√4)? - (√4)? 79 = ((√4)?) ^ 4 + √4 - 4 80 = (44 - 4) × √4 81 = ((√4)?) ^ 4 + 4 - 4 82 = ((√4)?) ^ 4 + 4 / 4 83 = ((√4)?) ^ 4 + 4 - √4 84 = 44 × √4 - 4 85 = 44 × √4 - (√4)? 86 = 44 × √4 - √4 87 = (4 + √4)? × 4 + (√4)? 88 = 44 × 4 / √4 89 = ((√4)?) ^ 4 + 4 + 4 90 = 44 × √4 + √4 91 = 44 × √4 + (√4)? 92 = 44 × √4 + 4 93 = (4?) × (4?) - 4 - (√4)? 94 = (4?) × (4?) - 4 - √4 95 = (4?) × (4?) - √4 - (√4)? 96 = (4?) × (4?) - √4 - √4 97 = (4?) × (4?) + (√4)? - ((√4)?)? 98 = (4?) × (4?) - ((√4)?)? / (√4)? 99 = (4?) × (4?) - 4 / 4 100 = ((√4 + √4)?) × ((√4 + √4)?)

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Posted: 8/23/2005 9:41 PM

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nesrocks

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101 = 4? * 4? + 4/4 102 = 4? * 4? + 4 - √4

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Posted: 8/23/2005 9:53 PM

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Randil

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doh, you were minutes faster Dacicus :)

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Posted: 8/23/2005 9:54 PM

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Bag_of_Magic_Food

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Did anyone post a replacement 31?

put yourself in my rocketpack if that poochie is one outrageous dude

Posted: 8/23/2005 9:54 PM

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Dacicus

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103 = 4? × 4? + ((√4)?)? - (√4)? 104 = 4? × 4? + √4 × √4 105 = 4? × 4? + √4 + (√4)? 106 = 4? × 4? + 4 + √4 107 = 4? × 4? + 4 + (√4)? 108 = 4? × 4? + 4 + 4 109 = 4? × 4? + (√4)? × (√4)? 110 = 4? × 4? + (√4 + √4)? 31 has been completed. I think it's on the first page. EDIT: If it's not, then 4? × 4? / 4 + ((√4)?)? works.

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Posted: 8/23/2005 10:02 PM
(Edited: 8/23/2005 10:08 PM)

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Randil

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Bag of Magic Food wrote:

Did anyone post a replacement 31?

Yes, I did that earlier today, but here it is again: 31 = (sqrt4+sqrt4+sqrt4)? + 4? and here's another way to do it: 31 = ((sqrt4+sqrt4)?)? -(sqrt4+sqrt4)! By the way, how far are wo gonna go with this? Not that I mind if we continue or anything, I'm just wondering.

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Posted: 8/23/2005 10:06 PM

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Dacicus

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As far as possible, I guess. 112 = 4? × 4? + (√4)? × 4

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Posted: 8/23/2005 10:07 PM

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nesrocks

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112 = (4! + √4 + √4) * 4

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Posted: 8/23/2005 10:09 PM

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Randil

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111 = (4?)? + (4?)? + (4/4) 112 = (4?)? + (4?)? + 4 - sqrt4 113 = (4? + 4)? + 4 + 4 114 = (4? + sqrt4)? + (4+4)? 115 = (4? + 4)? + (sqrt4+sqrt4)? 116 = (4?)? + (4?)? + 4 + sqrt4

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Posted: 8/23/2005 10:10 PM
(Edited: 8/23/2005 10:13 PM)

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Randil

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117 = (4? + 4)? + sqrt4 + 4? 118 = (4? + sqrt4)? + 4*(4?) 119 = 4! + (4? + 4)? - 4? 120 = 4!*(4+(4/4))

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Posted: 8/23/2005 10:13 PM

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nesrocks

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117 = (√4)? * 4 * 4? - √4?

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Posted: 8/23/2005 10:14 PM

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Randil

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121 = (4? + 4)? + (4*4) By the way, how do you do the root-symbols?

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Posted: 8/23/2005 10:16 PM
(Edited: 8/23/2005 10:18 PM)

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nesrocks

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copy √4 and paste anyway you skipped 119 and 120... edit: oops. nm 122 = (√4)? * 4 * 4? + √4 123 = (√4)? * 4 * 4? + (√4)? 124 = (√4)? * 4 * 4? + 4

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Posted: 8/23/2005 10:18 PM

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Randil

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122 = √4*((4?)?) + 4? +√4 It's starting to get difficult now... :) BTW, thanks FODA for the telling me about the root-symbol 125 =( 4? + 4)? + √4*4? 126 = (4? + 4)? + 4*4

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Posted: 8/23/2005 10:22 PM

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