Four digits
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Other results: Four fours Three fours Four zeros 2002 2003
The following solutions are correct for any positive digit d. Solutions are shown, where known, for numbers in the range 0–100. Solutions are known for 76 of the 101 numbers. The first number for which no solution has been found is 14.
These solutions were generated manually, not by 200 Up. I’d be interested in hearing from anyone who finds a solution for a number for which no solution is known.
0 = dd - dd
1 = dd / dd
2 = (d / d) + (d / d)
3 = (d + d + d) / d
4 = sqrt(d / .d~) + (d / d)
5 = sqrt(d * d) / (.d + .d)
6 = (d / .d~) - sqrt(d / .d~)
7 = (d / .d) - sqrt(d / .d~)
8 = (d / .d~) - (d / d)
9 = (d / .d) - (d / d)
10 = dd / d.d
11 = (d / .d) + (d / d)
12 = (d / .d~) + sqrt(d / .d~)
13 = (d / .d) + sqrt(d / .d~)
14
15 = sqrt(sqrt(d * d)) / (sqrt(.d~%) + sqrt(.d~%))
16 = (d / .d) + sqrt(d / .d~)!
17 = (d + d - .d~) / .d~
18 = (d / .d~) + (d / .d~)
19 = (d / .d) + (d / .d~)
20 = (d / .d) + (d / .d)
21 = sqrt(d / .d~%) - (d / .d~)
22
23 = (sqrt(d) - sqrt(.d~)%) / (sqrt(.d~%) + sqrt(d)%)
24 = (sqrt(d) - (sqrt(d%) + sqrt(d%))) / sqrt(.d~%)
25 = sqrt(.d~) / ((sqrt(sqrt(d * d)) + sqrt(.d~))%)
26 = (sqrt(d) - (sqrt(d%) + sqrt(.d~%))) / sqrt(.d~%)
27 = (d / .d~) * sqrt(d / .d~)
28 = (sqrt(d) - (sqrt(.d~%) + sqrt(.d~%))) / sqrt(.d~%)
29 = sqrt(d / .d~%) - (d / d)
30 = (d / .d) * sqrt(d / .d~)
31 = sqrt(d / .d~%) + (d / d)
32 = (sqrt(d) + sqrt(.d~%) + sqrt(.d~%)) / sqrt(.d~%)
33 = sqrt(d / .d~%) + sqrt(d / .d~)
34 = (sqrt(d) + sqrt(d%) + sqrt(.d~%)) / sqrt(.d~%)
35 = (sqrt(.d~%) - sqrt(d)%) / ((sqrt(.d~%) + sqrt(.d~%))%)
36 = (sqrt(d) + sqrt(d%) + sqrt(d%)) / sqrt(.d~%)
37 = (sqrt(d) + sqrt(.d~) - sqrt(d%)) / sqrt(.d~%)
38
39 = sqrt(d / .d~%) + (d / .d~)
40 = sqrt(d / .d~%) + (d / .d)
41 = (sqrt(d) + sqrt(.d~) + sqrt(.d~%)) / sqrt(.d~%)
42
43 = (sqrt(d) + sqrt(.d~) + sqrt(d%)) / sqrt(.d~%)
44
45 = (.d - d%) / (.d% + .d%)
46
47
48
49
50 = (sqrt(d) + sqrt(.d~) + sqrt(.d~)) / sqrt(.d~%)
51
52
53
54 = (d / .d~) * sqrt(d / .d~)!
55 = dd / (.d + .d)
56
57 = (sqrt(d) + sqrt(d) - sqrt(d%)) / sqrt(.d~%)
58
59 = (sqrt(d) + sqrt(d) - sqrt(.d~%)) / sqrt(.d~%)
60 = sqrt(d / .d~%) + sqrt(d / .d~%)
61 = (sqrt(d) + sqrt(d) + sqrt(.d~%)) / sqrt(.d~%)
62
63 = (sqrt(d) + sqrt(d) + sqrt(d%)) / sqrt(.d~%)
64
65 = (sqrt(.d~%) + sqrt(d)%) / ((sqrt(.d~%) + sqrt(.d~%))%)
66
67 = (sqrt(.d~%) - (sqrt(d) + sqrt(d%))%) / sqrt(.d~%)%
68
69 = (sqrt(.d~%) - (sqrt(d) + sqrt(.d~%))%) / sqrt(.d~%)%
70 = (d / d%) - sqrt(d / .d~%)
71 = (sqrt(.d~%) + (sqrt(.d~%) - sqrt(d))%) / sqrt(.d~%)%
72 = (.d * sqrt(d / .d~)!!) / d
73 = (sqrt(.d~%) + (sqrt(d%) - sqrt(d))%) / sqrt(.d~%)%
74
75 = sqrt(sqrt(d * d)) / ((sqrt(d) + sqrt(.d~))%)
76
77 = (sqrt(.d~) + sqrt(.d~%)%) / ((sqrt(.d~) + sqrt(d%))%)
78
79
80 = (.d / .d~%) - (d / .d)
81 = (d / .d~) * (d / .d~)
82 = (.d + .d~% - d%) / .d~%
83
84 = (.d / .d~%) - sqrt(d / .d~)!
85
86
87 = (.d / .d~%) - sqrt(d / .d~)
88 = (.d - (.d~% + .d~%)) / .d~%
89 = (.d / .d~%) - (d / d)
90 = (d / .d) * (d / .d~)
91 = (.d / .d~%) + (d / d)
92 = (.d + .d~% + .d~%) / .d~%
93 = (.d / .d~%) + sqrt(d / .d~)
94 = (sqrt(.d~) - (sqrt(d) + sqrt(d))%) / sqrt(.d~)%
95 = (.d~ + .d) / (.d~% + .d~%)
96 = (sqrt(.d~) - (sqrt(d) + sqrt(.d~))%) / sqrt(.d~)%
97 = (d / d%) - sqrt(d / .d~)
98 = (dd - .d~) / .d~
99 = (d / d%) - (d / d)
100 = (d / .d) * (d / .d)
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Other results: Four fours Three fours Four zeros 2002 2003
