 mersenneforum.org Classic problem: Four 4's
 Register FAQ Search Today's Posts Mark Forums Read  2005-09-28, 22:45 #12 akruppa   "Nancy" Aug 2002 Alexandria 9A316 Posts 12 = 4sq-4 40 = 4sq/.4   2005-09-28, 23:03 #13 grandpascorpion   Jan 2005 Transdniestr 503 Posts Thru 75, I'm having some trouble computing the following: 38, 42, 55, 57, 58, 62, 67 and 75   2005-09-28, 23:18   #14
rogue

"Mark"
Apr 2003
Between here and the

23·5·7·23 Posts Quote:
 Originally Posted by grandpascorpion Thru 75, I'm having some trouble computing the following: 38, 42, 55, 57, 58, 62, 67 and 75
38 = 4! + 4/.4 + 4

42 = 4! + 4! - 4!/4

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

I wonder how difficult it would be to write a program to evaluate all possible expressions (given the limitations) and output the simplest solution for each, i.e. the one that uses the fewest 4's.   2005-09-28, 23:25 #15 rogue   "Mark" Apr 2003 Between here and the 23·5·7·23 Posts    2005-09-28, 23:29 #16 grandpascorpion   Jan 2005 Transdniestr 503 Posts Ah but many of those solutions use the square root sign (which is verboten under Ken's rules). Last fiddled with by grandpascorpion on 2005-09-28 at 23:30   2005-09-29, 00:33 #17 rogue   "Mark" Apr 2003 Between here and the 144508 Posts Here are some others without resorting to the link I produced above. If they are the same, it is coincidental. There are multiple solutions to many of these. Many of the ones below follow easily from other solutions. 59 = 4!/.4 - 4/4 61 = 4!/.4 + 4/4 66 = 4!/.4 + 4!/4 68 = 4!/.4 + 4 + 4 68 = 4! + 4! + 4! - 4 70 = (4 + 4)!/(4! * 4!) 76 = 4! + 4! + 4! + 4 82 = 4!/.4 + 4! - 4 86 = 4!/.4 + 4! 90 = 4!/.4 + 4! + 4 92 = 4! * 4 - 4 95 = 4! * 4 - 4/4 97 = 4! * 4 + 4/4 101 = (4/.4)sq + 4/4 104 = (4/.4)sq + 4 108 = (4/.4)sq + 4 + 4 116 = (4+4/4)! - 4 117 = (44/4)sq - 4 124 = (4+4/4)! + 4 125 = (44/4)sq + 4 128 = 4!sq/4 - 4sq 132 = 4!sq/4 - 4sq + 4 136 = 4!sq/4 - 4 - 4 140 = 4!sq/4 - 4 143 = 4!sq/4 - 4/4 144 = 4!sq/4 + 4/4   2005-09-29, 00:34 #18 rogue   "Mark" Apr 2003 Between here and the 11001001010002 Posts Here is the current list to save everyone from scrolling. It contains duplicates as those might provide ideas for expanding the table. 0 = 4-4 1 = 4/4 2 = (4+4)/4 3 = (4+4+4)/4 4 = 4 5 = 4 + 4/4 6 = 4! / 4 7 = (4!+4)/4 7 = 4 + 4 - 4/4 8 = 4 + 4 9 = 4 + 4 + 4/4 10 = 4 / .4 11 = 44 / 4 12 = 4 + 4 + 4 12 = 4sq-4 13 = 4sq -4 + 4/4 14 = 4sq - (4+4)/4 15 = 4sq - 4/4 16 = 4sq 17 = 4sq + 4/4 18 = 4/.4 + 4 + 4 19 = 4! - 4 - 4/4 20 = 4! - 4 21 = 4! -4 + 4/4 22 = 4! - (4+4)/4 23 = 4! - 4/4 24 = 4! 25 = 4! + 4/4 26 = 4sq + 4/.4 27 = 4! + 4 - 4/4 28 = 4sq + 4sq - 4 29 = 4! + 4 + 4/4 30 = (4+4/4)!/4 31 = 4sq + 4sq - 4/4 32 = 4sq + 4sq 33 = 4sq + 4sq + 4/4 34 = 4! + 4/.4 35 = 4! + 44/4 36 = 4!sq / 4sq 37 = 4!sq / 4sq + 4/4 38 = 4! + 4/.4 + 4 39 = 4! + 4sq - 4/4 40 = 4! + 4sq 40 = 4sq/.4 41 = 4! + 4sq + 4/4 42 = 4! + 4! - 4!/4 43 = 44 - 4/4 44 = 44 45 = 44 + 4/4 47 = 4! + 4! - 4/4 48 = 4! + 4! 49 = 4! + 4! + 4/4 52 = 4! + 4! + 4 56 = 4*4sq-4-4 58 = 4! + 4! + 4/.4 59 = 4!/.4 - 4/4 60 = 4!/.4 60 = 4*4sq-4 61 = 4!/.4 + 4/4 63 = 4*4sq-4/4 64 = 4sq * 4 65 = 4*4sq+4/4 66 = 4!/.4 + 4!/4 68 = 4! + 4! + 4! - 4 68 = 4!/.4 + 4 + 4 70 = (4 + 4)!/(4! * 4!) 72 = 4! * 4 - 4! 76 = 4! + 4! + 4! + 4 80 = 4sq * 4 + 4sq 81 = ((4-4/4)sq)sq 82 = 4!/.4 + 4! - 4 86 = 4!/.4 + 4! 90 = 4!/.4 + 4! + 4 92 = 4! * 4 - 4 95 = (4! * 4sq-4)/4 95 = 4! * 4 - 4/4 96 = 4! * 4 96 = 4! * 4sq/4 97 = (4! * 4sq+4)/4 97 = 4! * 4 + 4/4 100 = ( 4 / .4 )sq 101 = (4/.4)sq + 4/4 104 = (4/.4)sq + 4 108 = (4/.4)sq + 4 + 4 109 = (44 -.4)/.4 110 = 44 / .4 111 = 44.4 / .4 116 = (4+4/4)! - 4 117 = (44/4)sq - 4 120 = (4+4/4)! 121 = (44/4)sq 124 = (4+4/4)! + 4 125 = (44/4)sq + 4 128 = 4!sq/4 - 4sq 128 = 4sq * 4 + 4sq * 4 132 = 4!sq/4 - 4sq + 4 136 = 4!sq/4 - 4 - 4 140 = 4!sq/4 - 4 143 = 4!sq/4 - 4/4 144 = 4!sq / 4 144 = 4!sq/4 + 4/4 256 = 4sq * 4sq   2005-09-29, 00:55 #19 rogue   "Mark" Apr 2003 Between here and the 144508 Posts And some more: 3 = 4 - 4/4 50 = 4sqsq - 4/.4 - 4 53 = 4sqsq - 44/4 54 = 4sqsq - 4/.4 54 = 4!/.4 - 4!/4 54 = 4! + 4! + 4!/4 55 = 4sqsq - (4 - 4/4)sq 57 = 4sqsq - (4!+4)/4 62 = 4sqsq - (4+4)/4 64 = 4sqsq 67 = 4sqsq + 4 - 4/4 69 = 4sqsq + 4 + 4/4 71 = 4sqsq + (4!+4)/4 73 = 4sqsq + (4 - 4/4)sq 74 = 4sqsq + 4/.4 75 = 4sqsq + 44/4 78 = 4sqsq + 4/.4 + 4 79 = 4sqsq + 4sq - 4/4 81 = 4sqsq + 4sq + 4/4 84 = 4sq * 4 + 4sq + 4 87 = 4sqsq + 4! - 4/4 89 = 4sqsq + 4! + 4/4 94 = (4/.4)sq - 4!/4 99 = (4/.4)sq - 4/4 102 = 4! * 4 + 4!/4 106 = (4/.4)sq + 4!/4 112 = 4! * 4 + 4sq 114 = 44/.4 + 4 Last fiddled with by rogue on 2005-09-29 at 01:03   2005-09-29, 00:59 #20 grandpascorpion   Jan 2005 Transdniestr 503 Posts S'more 46 = (4sq+4)/.4-4 50 = (4sq+4)/.4 51 = (4sq+4+.4)/.4 53 = ((4!+4)/4)sq+4 54 = (4sq+4)/.4+4 69 = (4!+4-.4)/.4 71 = (4!+4+.4)/.4 74 = (4!+4)/.4+4 84 = 4*(4sq+4)+4 94 = ( 4 / .4 )sq-4!/4 99 = ( 4 / .4 )sq-4/4 106 = ( 4 / .4 )sq+4!/4 112 = 4*(4!+4) edit : sorry, there's redundancies Last fiddled with by grandpascorpion on 2005-09-29 at 01:00   2005-09-29, 01:07 #21 rogue   "Mark" Apr 2003 Between here and the 23·5·7·23 Posts How did I miss this one: 88 = 4sqsq + 4! and 77 = (4 - 4/4)sqsq - 4 85 = (4! + 4/.4)/.4 (this one is a cheat from the link I provided) 85 = (4 - 4/4)sqsq + 4 (this one is mine) 98 = 4sqsq + 4! + 4/.4 105 = (4 - 4/4)sqsq + 4! That leaves 83, 91, 93, and 107 without solutions under 110. Last fiddled with by rogue on 2005-09-29 at 01:22   2005-09-29, 01:37 #22 S80780   Jan 2003 far from M40 53 Posts 0 = 4-4 1 = 4/4 2 = (4+4)/4 3 = 4-4/4 4 = 4 5 = 4+4/4 6 = 4+(4+4)/4 = 4/.4-4 = 4!/4 7 = 4+4-4/4 = (4!+4)/4 8 = 4+4 9 = (4-.4)/.4 10 = 4/.4 11 = 44/4 12 = 4^2-4 13 = 4^2-4+4/4 = (4!+4!+4)/4 14 = 4^2-(4+4)/4 15 = 4^2-4/4 16 = 4^2 17 = 4^2+4/4 18 = 4^2+(4+4)/4 19 = (4+4-.4)/.4 20 = (4+4)/.4 21 = (4+4.4)/.4 22 = 4!-(4+4)/4 23 = 4!-4/4 24 = 4! 25 = 4!+4/4 26 = 4!+(4+4)/4 27 = 4!+4-4/4 28 = 4!+4 29 = 4!+4+4/4 30 = (4+4/4)!/4 = (4+4+4)/.4 31 = 4^2+4^2-4/4 32 = 4^2+4^2 33 = 4^2+4^2+4/4 34 = 4! + 4/.4 35 = 4! + 44/4 36 = 4*(4-.4)/.4 = (4!/4)^2 37 = (4!/4)^2 + 4/4 38 = (4^2-.4-.4)/.4 39 = (4^2-.4)/.4 40 = 4^2/.4 41 = (4^2+.4)/.4 42 = (4^2+.4+.4)/.4 43 = 44-4/4 44 = 44 45 = 44+4/4 47 = 4!+4!-4/4 48 = ((4!+4)^2-4^2)/4^2 = 4!*(4+4)/4 = 4*(4^2-4) = 44+4 = 4!+4! 49 = (4+4-4/4)^2 = 4!+4!+4/4 = ((4!+4)/4)^2 50 = ((4!+4)^2+4^2)/4^2 = (4!-4)/.4 51 = (4!-4+.4)/.4 52 = 44+4+4 = 4!+4!+4 53 = ((4!+4)/4)^2+4 55 = (4!-.4)/.4-4 56 = 4!+4!+4+4 = 4!/.4-4 57 = (4!+.4)/.4-4 58 = (4!-.4-.4)/.4 59 = (4!-.4)/.4 60 = 4!/.4 61 = (4!+.4)/.4 62 = (4!+.4+.4)/.4 63 = 4*4^2-4/4 64 = 4*4^2 = (4+4)^2 65 = 4*4^2+4/4 = ((4!+4)/4)^2+4^2 68 = 4!+44 69 = (4!+4-.4)/.4 70 = (4!+4)/.4 71 = (4!+4.4)/.4 72 = 4!+4!+4! 74 = (4!+4)/.4+4 76 = 4!+4!+4!+4 80 = (4!+4+4)/.4 = (4^2-4)^2-(4+4)^2 = 4*(4!-4) 81 = ((4-.4)/.4)^2 84 = 4*(4!-4)+4 = 4!/.4+4! 85 = ((4-.4)/4)^2+4 = (4!+.4)/.4+4! 88 = 4!+4!+4!+4^2 92 = (4/.4)^2-4-4 = 4*4!-4 95 = 4!*4-4/4 96 = 4!*4 97 = 4!*4+4/4 99 = (4/.4)^2-4/4 100 = 4*4!+4 = (4/.4)^2 101 = (4/.4)^2+4/4 104 = (4/.4)^2+4 105 = (44/4)^2-4^2 106 = 44/.4-4 108 = (4/.4)^2+4+4 109 = (44-.4)/.4 110 = 44/.4 111 = 444/4 112 = (4^2-4)^2-4^2-4^2 114 = 44/.4+4 116 = (4/.4)^2+4^2 117 = (44/4)^2-4 119 = (4!+4!-.4)/.4 120 = (4+4/4)! = (4!+4!)/.4 121 = (44/4)^2 124 = (4^2-4)^2-4^2-4 125 = (44/4)^2+4 = (4!-4)/(.4)^2 128 = (4^2-4)^2-4^2 132 = (4/.4)^2+4^2+4^2 = (4^2-4)^2-4^2+4 136 = (4^2-4)^2-4-4 137 = (44/4)^2+4^2 138 = (4!^2-4!)/4 140 = (4^2-4)^2-4 142 = (4!^2-4-4)/4 143 = (4^2-4)^2-4/4 = (4!^2-4)/4 144 = (4^2-4)^2 = 4!^2/4 145 = (4^2-4)^2+4/4 = (4!^2+4)/4 146 = (4!^2+4+4)/4 148 = (4^2-4)^2+4 149 = (4!-(.4)^2)/(.4)^2 150 = 4!/(.4)^2 151 = (4!+(.4)^2)/(.4)^2 152 = (4^2-4)^2+4+4 = 4*44-4! 153 = 4+(4!-(.4)^2)/(.4)^2 154 = 4+4!/(.4)^2 155 = 4+(4!+(.4)^2)/(.4)^2 160 = (4^2-4)^2+4^2   Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post davieddy PrimeNet 26 2011-06-13 09:38 davieddy PrimeNet 6 2009-10-04 08:33 ian209 Hardware 4 2006-02-18 19:52 fetofs Puzzles 7 2005-10-16 11:45 JuanTutors Puzzles 24 2005-08-28 23:46

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