# Representation of numbers with four 3's

 1 3·3/3/3 2 (3+3)/(√3·√3) 3 (3+3+3)/3 = 33/3/3 4 √3·√3+3/3 = 3!-(3+3)/3 5 3!-(√3·√3)/3 = (3+3)/3+3 6 3!+(3-3)/3 7 3!+(√3·√3)/3 8 [3·√3]+√3·√3 9 3·3·3/3 10 3·3+3/3 11 [(√3+3)·3-3] = 3!+3!-3/3 = 3/.3+3/3 12 3+3+3+3 13 3!+3!+3/3 14 3·3+[3·√3] 15 3·3+3+3 = (3!-3/3)·3 16 3/.3+3+3 17 3·3!-3/3 18 3·3!-3+3 = (3!-3/3)!!+3 = 33-3·3 = 3·3+3·3(2) 19 3·3!+3/3 20 3/.3+3/.3 21 33-3-3 22 (3!)!!/3+3+3 23 (3+3)/.3+3 24 3·3!+3+3 25 [3·3·3-√3] 26 33-3/3 27 33-3+3 = 33!/3·3(3) 28 33+3/3 = [3·3/.3 - √3] = 33+3/3(3) = (√(3!)!! + 3!·√(3!)!!)/√3(3) 29 3·3/.3-[√3]=3!/.3+3·3 = 33+3!/3(3) 30 3·3·3+3 = 3!·3!-3-3 = 33+3!-3= 3·3·3+3(3) = ((3!)!!+(3!)!!-3!)/3(3) = (3!)!!-3!·√3·3(3) = (3!)3/3!-3!(3) 31 3·3/.3+[√3] = 33-3!/3(3) = ((3!)!!+(3!)!!-3)/3(3) 32 33-3/3 = (3!)!!/3·3!/3(3) 33 33-3+3 = 33/3·3(3) = 33+3+3(3) = 3!·3!-3!+3(3) = (3!)3!/3-3(3) = 3·√3·(3!)!! - 3(3) = ((3!)!!+(3!)!!+3)/3(3) = (3!)3/3!-3(3) 34 33+3/3 = 3!·3!-3!/3(3) = ((3!)!!+(3!)!!+3!)/3(3) 35 33+3!/3(1)= 3!·3!-3/3(3) = ((3!)!!+(3!)!!)/3+3(3) 36 33 + √3·3 = 33+3·3(3) = 3!·3!+3-3(3) = 33+3·3(3) = √3!·3!·3!·3!(3) 37 3!·3!+3/3(3) = (3!)!!-33/3(3) 38 3!·3!+3!/3(3) 39 33+3+3(3) = 3!·3!+3!-3(3) = (3!)!!-33!/3(3) = (3!)3!/3+3(3) = 3·√3·(3!)!! + 3(3) = (3!+3!)·3+3(3) = (3!)3/3!+3(3) 40 (3+3!/3)!/3(3) = (3!)!!-3!-3!/3(3) = (3!)!!-(3!/3)3(3) = 3!/3·3!/.3(3) 41 (3!)!!-3!-3/3(3) 42 (3!)!!-3·3+3(3) = 3!·3!+3+3(3) = 3!·(3!+3/3)(3) = 33+3·3(3) = (3!)3/3!+3!(3) = 33/.3-(3!)!!(3) 43 (3!)!!-3!+3/3(3) = (3!)!!-3!/3-3(3) 44 (3!)!!-3!+3!/3(3) = (3!)!!-3-3/3(3) 45 (3!)!!+3-3-3(3) = 3·(3+3!/3)!!(3) 46 (3!)!!-3+3/3(3) = (3+3)!!-3!/3(3) = (3!)!! - √3 + 3/3(3) = (3!)!! - √3! - 3!/3(3) 47 (3!)!!-3+3!/3(3) = (3!)!!-(3/3)3(3) = 33+3!/.3(3) 48 (3!)!!+3!-3-3(3) = ((3!)!!+(3!)!!+(3!)!!)/3(3) = 3·3·3!-3!(3) 49 (3!)!!+3-3!/3(3) = (3!)!!+(3/3)3(3) 50 (3!)!! + √3 + 3/3(3) = (3!)!! + √3! - 3!/3 = (3!)!!+(3!)!!/3!-3!(3) 51 (3!)!!+3+3-3(3) = (3!)!!+3·3/3(3) = 3·3·3!-3(3) 52 (3!)!!+3+3/3(3) = (3!)!!+3!-3!/3(3) = (3!)!!+3/.3-3!(3) 53 (3!)!!+3+3!/3(3) = (3!)!!+(3!)!!/3!-3(3) = 33+3!/.3(3) 54 (3!)!!+3!+3-3(3) = (3!)!!+3!·3!/3!(3) = 33·3!/3(3) = 33+33(3) = 3!·3!+3·3!(3) = 3!·3/.3-3!(3) 55 (3!)!!+3!+3/3(3) = (3!)!!+3/.3-3(3) 56 (3!)!!+(3+3/3)!!(3) = (3!)!!+3!+3!/3(3) = (3!)!!+(3!/3)3(3) = 3!·3!+3!/.3(3) 57 (3!)!!+33/3(3) = (3!)!!+3!+3!-3(3) = 3·3·3!+3(3) = 3!·3/.3-3(3) 58 (3!/3)3!-3!(3) 59 (3!)!!+33/3(3) = (3!)!!+(3!)!!/3!+3(3) 60 (3!)!!+3!·3!/3(3) = (3!)!!+3·3+3(3) = (3!)!!+(3!)!!-3!·3!(3) = (3!)!!+3·3!-3!(3) = 3·3·3!+3!(3) = 33+33(3) 61 (3!/3)3!-3(3) = (3!)!!+(3!)!!/3-3(3) = (3!)!!+3/.3+3(3) 62 (3!)!!+(3!)!!/3!+3!(3) = (3!)!!+3!/.3-3!(3) = 33/.3-(3!)!!(3) 63 (3!)!!+3·3+3!(3) = (3!)!!+3!+3!+3(3) = 3!·3/.3+3(3) = 33+3!·3!(3) = (33-3!)·3(3) = 3!·3/.3+3(3) 64 (3+3/3)3(3) = (3!-3!/3)3(3) = ((3!)!!/3!)·((3!)!!/3!)(3) = ((3!)!!/3!)3!/3(3) = (3!)!!+3/.3+3!(3) = (3!)!!/.3-(3!)!!-(3!)!!(3) 65 (3!)!!+3!/.3-3(3) 66 33·3!/3 = 33+33(3) = (3!)!!+3!+3!+3!(3) = √3·(3!)!!·3!-3!(3) = 3·3!/.3+3!(3) 67 (3!/3)3!+3(3) = (3!)!!+(3!)!!/3+3(3) 68 (3!)!!+(3+3)/.3(3) = 3!<<3+3!/.3(3) 69 (3!)!!+3·3!+3(3) = √3·(3!)!!·3!-3(3) = (3!)!!+33-3!(3) = 33+3!·3!(3) 70 (3!/3)3!+3!(3) = (3!)!!+(3!)!!/3+3!(3) 71 (3!)!!+3!/.3+3(3) 72 3·3·(3!)!!/3!(3) = (33-3)·3(3) = (3!)!!+33-3(3) = 3!·3!+3!·3!(3) = (3!)3-3·(3!)!!(3) = (3!)!-3·(3!)3(3) = (3+3)·√3·(3!)!!(3) = 3!·3!/.3-(3!)!!(3) = (3+3/3)!·3

(1) By Andre Gustavo dos Santos from Brasil

(2) By Emiliano Venturini from Italy.