# 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

(3) By Denis Borris

(4) By Jim Bean

• Funny Arithmetic
• A single formula to express all numbers
• Any Integer with Three 2s
• Representation of numbers with a single 4. The rules and the possibilities
• One 4, a story
• Three 3's
• Representation of numbers with three 4's
• Representation of numbers with three 5's
• Representation of numbers with four 3's
• Representation of numbers with four 4's
• A problem of representing 4 by four identical digits
• A problem of representing 6 by three identical digits
• A 9's Fan's Clock
• Make an Identity
• Fun with numbers: place plus/minus signs between the digits
• 24 with One Digit
• Representation of 3 with Three Equal Digits
•