brianjn
2008-07-12 23:03:32 |
Four Fours
In 2005 Josh70679 gave us
"Five Fives" and discussion was carried further into a
forum discussion.
Pcbouhid gave us "The Five 3's" in 2008. In his problem text he mentions the classic "Four Fours" problem. In discussions with him he sent me a set of solutions, up to 100, for the "Four Fours" allowing me to use them as I felt best. That list follows. Please feel free to add comment. And thanks Paulo for this contribution. |
brianjn
2008-07-12 23:06:19 |
Re: Four Fours
A SOLUTION FOR THE "FOUR FOURS" CHALLENGE
PAULO BOUHID
Rio de Janeiro/Brasil
Besides the basic math operations, exponentiation, square root and factorial, we will use the dot (".") as the decimal point (so, .4 = 4/10), and a dot above the 4 in .4 will represent the periodic decimal .444444... = 4/9; we will denote this as .4'.
0 = 44 - 44 1 = 44/44
2 = 4/4 + 4/4 3 = (4 + 4 + 4)/4
4 = 4 + 4 - sqrt(4) - sqrt(4) 5 = (4 x 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 = 44/sqrt(4 x 4)
12 = (44 + 4)/4 13 = 44/4 + sqrt(4)
14 = 4 x 4 - 4/sqrt(4) 15 = 4 x 4 - 4/4
16 = 4 x 4 + 4 - 4 17 = 4 x 4 + 4/4
18 = 4 x 4 + 4 - sqrt(4) 19 = 4! - (4 + 4/4)
20 = 4! + 4 - 4 - 4 21 = 4! + 4/4 - 4
22 = 44/(4 - sqrt(4)) 23 = 4! - (4 - sqrt(4))/sqrt(4)
24 = 4 x 4 + 4 + 4 25 = 4! + (sqrt(4) + sqrt(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)/4
32 = 4! + 4 + sqrt(4) + sqrt(4) 33 = 4! + (sqrt(4 x 4)/.4')
34 = 4! + 4 + 4 + sqrt(4) 35 = 4! + 44/4
36 = 4! + 4 + 4 + 4 37 = 4! + 4 + 4/.4'
38 = 4! + 4 x 4 - sqrt(4) 39 = 4! + 4! - 4/.4'
40 = 44 - sqrt(4) - sqrt(4) 41 = 44 - sqrt(4/.4')
42 = 4! + 4 x 4 + sqrt(4) 43 = 44 - 4/4
44 = 44 + 4 - 4 45 = 44 + 4/4
46 = 44 + 4 - sqrt(4) 47 = 44 + sqrt(4/.4')
48 = 4! + 4! + 4 - 4 49 = 4! + 4! + 4/4
50 = 4! + 4! + 4 - sqrt(4) 51 = 4! + 4! + sqrt(4/.4')
52 = 4! + 4! + sqrt(4) + sqrt(4) 53 = 44 + 4/.4'
54 = 4! + 4! + 4 + sqrt(4) 55 = 4!/.4' + 4/4
56 = 4! + 4! + 4 + 4 57 = 4! + 4! + 4/.4'
58 = (44 - 4!)/4 59 = (4! + 4)/.4' - 4
60 = 44 + 4 x 4 61 = (4! + 4)/.4' - sqrt(4)
62 = (44/4) - sqrt(4) 63 = (44 - 4)/4
64 = 44 + 4! - 4 65 = (44 + 4)/4
66 = 44 + 4! - sqrt(4) 67 = (4! + 4)/.4' + 4
68 = 4! + 4! + 4! - 4 69 = (4! + 4 - .4)/.4
70 = (44 + 4!)/4 71 = (4! + 4.4)/.4
72 = 4! x (4 - 4/4) 73 = sqrt(sqrt(sqrt(44!))) + 4/.4'
74 = 4! + 4! + 4! + sqrt(4) 75 = 44/.4' - 4!
76 = 4! + 4! + 4! + 4 77 = (4/.4´)sqrt(4) - 4
78 = 4 x (4! - 4) - sqrt(4) 79 = (4/.4´)sqrt(4) - sqrt(4)
80 = 4 x (4 x 4 + 4) 81 = (4 - 4/4)4
82 = 4 x (4! - 4) + sqrt(4) 83 = (4/.4´)sqrt(4) + sqrt(4)
84 = 44 x sqrt(4) - 4 85 = (4/.4´)sqrt(4) + 4
86 = 44 x sqrt(4) - sqrt(4) 87 = 4 x 4! - 4/.4'
88 = 44 + 44 89 = (4! + sqrt(4))/.4 + 4!
90 = 4 x 4! - 4 - sqrt(4) 91 = 4 x 4! - sqrt(4)/.4
92 = 4 x 4! - sqrt(4) - sqrt(4) 93 = 4 x 4! - sqrt(4/.4')
94 = 4 x 4! - 4 + sqtr(4) 95 = 4 x 4! - 4/4
96 = 4 x 4! + 4 - 4 97 = 4 x 4! + 4/4
98 = 4 x 4! + 4 - sqrt(4) 99 = 4 x 4! + sqrt(4/.4')
100 = 4 x 4! + sqrt(4) + sqrt(4)
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pcbouhid
2008-07-14 00:34:48 |
Re: Four Fours
Ty for your support, Brian. Although there are various sites where solutions for the "four fours" challenge can be found, this one that you kindly post it´s MY solution. |
