Representation of numbers with four 5's

1 5/5×5/5 = 5×5-5!/5(2)
2 (5+5)/5/5 = 5!!-5!/5!!-5(2) = (5!!/5)!)!!×5/5!(2) = 5!/5!!-(5!!/5)!(2) = 5!!/5-5/5(2)
3 (5+5+5)/5 = 5!/5!!-(5×5)(2) = 5!!/5+5-5(2) = 5×5-5×.5(2)
4 5×5-5/5 = 5/.5-(5!!/5)!(2) = 5/5/.5/.5(2) = 5!!/5+5/5(2)
5 5×5/5/5 = (5+5)/.5-5!!(2) = (5!!/5)!-5/5(2)
6 5×5+5/5 = 55/5-5(2) = (5!!/5)!+5-5(2)
7 5+(5+5)/5 = 5!/(5+5)-5(2) = (5!!/5)!+5/5(2) = 55-((5!!/5)!)!!(2) = 55-((15/5)!)!!(2) = (5!!×5!!)×.5-.5(2) = (((5!!/5)!)!/5)-5(2)
8 5/.(5)-5/5 = 5!/5!!+5-5(2) = (5!!×5!!)×.5+.5(2) = 5!/(5+5+5)(3)
9 5/.5-5/5 = 5!!-5-5/5(2) = 5!!/5+5!!/5(2) = 5!!/5×5!!/5(2) = 5!/(5×5)-5!!(2) = 5+5-5/5(3)
10 5/.5+5-5=5/.(5)+5/5 = 5!!×.5+5×.5(2) = 5+5+5-5(2) = 55/5.5(2)
11 5+5+5/5 = 5!!-5+5/5(2) = 55/(5×5) = ((5!!/5)!-.5)/.5(2)
12 5+5+[.5×5] = 5!!-5!/5!!+5(2) = 5!/(5×5)×.5(2) = (((5!!/5)!)!/(5×5))(2)
13 (5+5)/.(5)-5=5!!-(5+5)/5 = 5!/5!!+(5×5)(2) = ((5!!/5)!+.5)/.5(2) = (5!-55)/5(3)
14 5+5+5-[5] = 5!/5-5/.5(2) = 5!/5-5!!+5(2) = 5!/5!!+(5!!/5)!(2) = 5!/5-5-5(3)
15 (5+5)/.5-5=5×5-5-5 = (5!/5!!-.5)/.5(2) = 5!!+5-(5×5)(2)
16 5×5-5/.(5) = 55/5+5(2) = (5!/5!!)!!/5!×5(2) = (5!!+.5)/.5-5!!(2)
17 [(5+5)/.5-5] = 5!!+(5+5)/5 = 5!/(5+5)+5(2) = 5×5-5!/5!!(2) = (5!!-5-.5)/.5(2) = (((5!!/5)!)!/5)+5(2) = (5!/5!!+.5)/.5(2) = 5!!/.(5)-5-5(2) = 5!!/.(5)-5!!+5(2) = (5!!/).(5)-.5)/.5(2)
18 5!!+5+5-5 = (5+5)/.5-[5] = 5!!+5!/5!!-5(2) = 5!/5!!+5+5(2) = (5!!/5)×(5!!/5)!(2) = 15/5×(15/5)!(2) = 5!!+(5!!/5)!×.5(2) = 5/.(5)+5/.(5)(2) = (5!-5)/5-5(3)
19 5/.5+5/.(5) = 5!!+5-5/5(2) = (5!!-5+.5)/.5(2) = (5!-5·5)/5
20 5/.5+5/.5 = 5!!+(5×5)(2) = 5!!/.5-5/.5(2) = 5!/5!!×5×.5(2)
21 5!!+5+5/5 = (5!!-5+.5)/.5-5!!(2) = ((5!!/5)!)!!-5!!/.(5)(2)
22 (5+5)/.5+[5] = 55/5/.5(2) = 5!!+5!!-5!/5!!(2) = (5!-5-5)/5(3)
23 (5+5)/.(5)+5 = 5!/5-5/5(2) = 5!/5!!+5!!(2) = ((5!!/5)!)!!-5×5(2)
24 5×5-5/5 = 5!/5+5-5(2) = 5!/5×5/5(2) = 5!!/.5-(5!!/5)!(2) = (5!!-.5)/.5-5(2)
25 5×5+5-5 = 5!/5+5/5(2) = (5×5×5×5)(2) = 5!/5!!×5-5!!(2) = (55-5)×.5(2) = (5!+5)×5(2)
26 5×5+5/5 = 5!!+55/5(2) = (5!/5!!+5)/.5(2) = (5!!+.5)/.5-5(2) = (5!+5+5)/5(3)
27 5!!/.(5)+5-5 = 5!!+5!!-5!!/5(2) = 5!!+(5!!/5)!/.5(2) = 55×.5-.5(2) = (((5!!/5)!)!/5)+5!!(2)
28 5!!/.(5)+5/5 = 5!!/.5-5+[5!](1) = 5!!+5!/5!!+5(2) = 55×.5+.5(2) = (5!!-5/5)/.5(2) = 55-5!!/.(5)(2)
29 5!!/.5-5/5 = 5!/5+(5×5)(2) = 5!!+5!!-5/5(2) = (5!+5·5)/5(3)
30 5!!/.5+5-5 = (5+5/5)×5 = 55-5×5 = (55+5)×.5 = 5!/5+(5!!/5)!(2)
31 5!!/.5+5/5 = 5!!/.5-5+[5!]!(1) = 5!!/.5+5/5(2) = 55-5!/5(2) = .5((5!!/5)!)-5(2)
32 5×5+5+[5] = 5!/5!!/.5/.5(2) = 5!/5+5!/5!!(2) = (5!!+5/5)/.5(2)
33 5!!/.5+5-[5] = 5!!+5!!+5!!/5(2) = 5!/5/.5-5!!(2) = 5.5×(5!!/5)!(2) = (5+.5)× (5!!/5)!(2)
34 5!!/.5+[5+5] = 5!/5+5/.5(2) = (5!!-.5)/.5+5(2) = 5!/5+5!!-5(2)
35 5×5+5+5 = 5!!/.5+5×5 = 55-5!!-5(2) = 5!/5!!×5-5(2) = 5!×.5-5×5(2) = (5!!×.5-.5)×5(2)
36 5!!/.(5)+5/.(5)=5!!/.5+5+[5]36 = (5!!/5)!×(5!!/5)!(2) = 5!!/.5+(5!!/5)!(2) = (5!!+.5)/.5+5(2)
37 5!!/.(5)+5+5 = 5!!×5×.5-.5(2) = 5!!/.(5)+5!!-5(2)
38 5!!+5×5-[5] = ((5!!/5)!)!!-5-5(2) = ((5!!/5)!)!!-5!!+5(2) = 5!!×5×.5+.5(2)
39 5!!+5×5-[5] = 5!/(5×5)+5!!(2) = (5!!+5-.5)/.5(2)
40 (5×5-5)/.5(1) = 5!!+5!!+5!!-5(2) = 5!!/.5+5/.5(2) = ((5!!/5)!)!!-5!/5!!(2) = 5/.5/.5/.5(2) = (5+5)/.5/.5(2) = (5!!×.5+.5)×5(2)
41 5!!+5×5+[5]41 = (5!!+5+.5)/.5(2) = (5!!+5.5)/.5(2) = .5((5!!/5)!)+5(2)
42 5!!+5×5+[5] = ((5!!/5)!)!!-(5!!/5)!(2)
43 ((5!!/5)!)!!-(5×5)(2) = 5!/5/.5-5(2)
44 5.5×5!/5!!(2) = (5+.5)×5!/5!!(2) = 5!/5+5!!+5(2)
45 55-5-5(2) = 55-5!!+5(2) = 5!/5!!×5+5(2) = ((5!!/5)!)!!-5!!/5(2) = 5×5/.5-5(2)
46 (5!!+.5)/.5+5!!(2) = 55-5/.(5)(2)
47 55-5!/5!!(2) = ((5!!/5)!)!!-5/5(2) = 55-5!/5!!(2) = 5!!/.(5)+5!!+5(2)
48 ((5!!/5)!)!!+5-5(2) = (5!!/5)!×5!/5!!(2) = (5!/5!!)!!/(5!/5!!)(2)
49 ((5!!/5)!)!!+5/5(2) = 55-(5!!/5)!(2) = 5!/5!!+5×5(2) = (5×5-.5)/.5(2) = .5(5!/5)-5!!(2)
50 55-(5×5)(2) = 5!!×5-5×5(2) = 5!!+5!!+5!!+5(2) = (5!-5!!-5)××.5(2) = (5!!×5+5!!)×.(5)(2)
51 ((5!!/5)!)!!+5!!/5(2) = 5!!×5-5!/5(2) = (5×5+.5)/.5(2) = 5!/5+5!!/.(5)(2)
52 55-5!!/5(2) = 5!×.5-5!/5!!(2) = (5!-5!!)×.5-.5(2)
53 ((5!!/5)!)!!+(5×5)(2) = 5!/5/.5+5(2) = (5!-5!!)×.5+.5(2) = (5!!/.(5)-.5)/.5(2)
54 55-5/5(2) = ((5!!/5)!)!!+(5!!/5)!(2) = 5!×.5-(5!!/5)!(2) = 5!/5+5!!+5!!(2) = 5!!/.(5)+5!!/.(5)(2)
55 55+5-5(2) = 5!×.5-(5×5)(2) = (5!!+5!!)/.5-5(2) = 5!!×5-15!!-5(2) = (5!-5!!+5)×.5(2) = 5×5/.5+5(2) = (5!!/.(5)+.5)/.5(2)
56 55+5/5(2) = ((5!!/5)!)!!+5!/5!!(2)
57 5!×.5-5!!/5(2) = (5!-5).5-.5(2) = 5!-((5!!/5)!)!!-5!!(2) = 5!!/.(5)+5!!+5!!(2)
58 55+5!!/5(2) = (5!-5)×.5+.5(2) = ((5!!/5)!)!!+5+5(2)
59 5!×.5-5/5(2) = (5!!+5!!-.5)/.5(2) = .5(5!/5)-5(2)
60 55+(5×5)(2) = 5!!/.5+5!!/.5(2) = (((5!!/5)!)!/5)×5(2) = (5×5!!×((5!!/5)!)!!)(2)
61 5!×.5+5/5(2) = 55+(5!!/5)!(2) = (5!!+5!!+.5)/.5(2)
62 (5!+5)×.5-.5(2)
63 55+5!/5!!(2) = 5!/5/.5+5!!(2) = 5!×.5+5!!/5(2) = (5!+5)×.5+.5(2)
64 5!/5!!×5!/5!!(2) = (5!/5!!)!!/(5!!/5)!(2) = 55+5/.(5)(2)
65 5!×.5+(5×5)(2) = (5!!+5!!)/.5+5(2) = 5!!/.5/.5+5(2)
66 5!×.5+(5!!/5)!(2) = (((5!!/5)!)!!-5!!)/.5(2) = 5!!/5-5/0.(5)(2) = .5(5/.(5))-5!!(2)
67 5!!×5-5!/5!!(2) = (5!+5!!)×.5-.5(2) = 5!-((5!!/5)!)!!-5(2)
68 5!×.5+5!/5!!(2) = (5!+5!!)×.5+.5(2)
69 5!!×5-(5!!/5)!(2) = .5(5!/5)+5(2)
70 5!!×(5×5)-5(2) = (5!+5!!+5)×.5(2)
71 ceiling((((5×5 + 5)5)))(3)
72 ((5!!/5)!)!!+5!/5(2) = 5!!×5-5!!/5(2) 72 = 5!!/5×5!/5(2) = ((5!!/5)!)!/5×.5(2)
73 5×5×ceiling(5) - [5](3)
74 5!!×5-5/5(2)
75 55+5!!+5(2) = 5!!×5+5-5(2) = 5!!×(5!!/5)!-5!!(2) = ((5!!/5)!)!!+5!!/.(5)(2) = (5 + 5 + 5)×5
76 5!!×5+5/5(2) = .5(5/.(5))-5(2)
77 5!-((5!!/5)!)!!+5(2)
78 ((5!!/5)!)!!+5!!/.5(2) = 5!!×5+5!!/5(2) = 5!-5!!/.(5)-5!!(2)
79 55+5!/5(2) = .5(5!/5)+5!!(2)
80 55+5×5(2) = 5!!×5+(5×5)(2) = (55-5!!)/.5(2) = (5×5-5!!)/.5(2) = 5!-5×5-5!!(2) = ((5!!/5)!)!/5×.(5)(2)
81 5!!×5+(5!!/5)!(2) = ((5!!/5)!)!!/.5-5!!(2) = 5×5/.(5)/.(5)(2)
82 55+5!!/.(5)(2)
83 5!!×5+5!/5!!(2)
84 5!-.5((5!!/5)!)(2)
85 5!!×5+5+5(2) = 5!!×(5!!/5)!-5(2)
86 (((5!!/5)!)!!-5)/.5(2) = .5(5/.(5)) + 5(2)
87 5!-((5!!/5)!)!!+5!!(2)
88 ceiling(55 × ((5))) + 5(3)
89 [(5!)] × (5 + 5) - ceiling((5!))(3)
90 [(5!)] × (5 + 5) - [(5!)](3)
91 [5]5 × ceiling[5] - 5(3)
92 5! - 5×5 - ceiling(5)(3)
93 5! - 5×5 - [5](3)
94 [5]5 × ceiling(5) - [5](3)
95 (5 + 5)[5] - 5(3)
96 [5]5 × (5 - [5])(3)
97 (5 + 5)[5] - ceiling[5](3)
98 (5 + 5)[5] - [5](3)
99 [5]5 × ceiling[5] + ceiling[5](3)
100 (5 + 5) × (5 + 5)(3) = 5! - 5 × 5 + 5(4)

(1) By Andre Gustavo dos Santos from Brasil

(2) By Vladimir Zajic

(3) By Denis Borris

(4) By Jim Bean


[an error occurred while processing this directive]

|Contact| |Front page| |Contents| |Up| |Arithmetic|

 

Copyright © 1996-2018 Alexander Bogomolny
[an error occurred while processing this directive]
[an error occurred while processing this directive]