USE FIVE ZEROES AND TRIGNO AND MATHS NOTATIONS TO MAKE 120 I really love this puzzle. This is nothing but just requires your presence of mind and some tricky use of mathematical and trigonometric operators. 1.) Make 120 with 5 zeros :- TRY AND SOLUTIONS SET DEEP BELOW Sol 1 :- (0! + 0! + 0! + 0! + 0!)! = 120 Here '!' symbol is used for factorial. And 0! = 1 = (0! + 0! + 0! + 0! + 0!)! = (1 + 1 + 1 + 1 + 1)! = 5! = 120 Sol 2 :- (cos (0) + cos (0) + cos (0) + cos (0) + cos (0))! = 120 = (cos (0) + cos (0) + cos (0) + cos (0) + cos (0))! = (1 + 1 + 1 + 1 + 1)! = 5! = 120 Similarly you can replace cos (0) with cot (0). Sol 3 :-(0!0! * 0!0!) - 0! = 120 = (0!0! * 0!0!) - 0! = (11 * 11) - 1 = 121 - 1 = 120 Sol 4 :- ((0! + 0!)^(0! + 0!) + 0!)! = 120 = ((0! + 0!)^(0! + 0!) + 0!)! = ((1 + 1)^(1 + 1) + 1)! = (2^2 + 1)! = (4 + 1)! = 5! = 120 Similarly you can do it in many ways. Seems quite easy. Isn't it. Lets make it a bit difficult. 2.) Make 120 with 4 zeros :- ((0! + 0! + 0!)! - 0!)! = 120 = ((0! + 0! + 0!)! - 0!)! = ((1 + 1 + 1)! - 1)! = (3! - 1)! = (6 - 1)! = 5! = 120 3.) Make 120 with 3 zeros :- Γ((0! + 0! + 0!)!) = 120 Here 'Γ' is called "Gamma Function". Γ (n) = (n - 1) ! , where n = 0, 1, 2, 3 , ....... = Γ((0! + 0! + 0!)!) = Γ((1 + 1 + 1)!) = Γ(3!) = Γ(6) = 5! = 120 4.) Make 120 with 1 zero :- Sol 1 :- sec ( tan-1 (…… sec ( tan-1 (0!)) ……)), with sec ( tan-1 ….) taken 14399 times = sqrt (14400) = 120 Consider a right-angled triangle with sides (1,1,√2). Thus, √2 = sec ( tan-1( 0! ) ) Now, consider a another right-angled triangle with sides (1,√2, √3). Here, √3 = sec ( tan-1 (sec ( tan-1( 0! ) ) ) ) Extrapolating this idea futher, for any number x, we can represent √x using one 0 as, √x = sec ( tan-1 (…… sec ( tan-1 (0!)) ……)), where sec ( tan-1 ….) is taken x-1 times Sol 2 :- (((((0!)++)++)++)++)! = 120 If you are known to programming then it'll be easy to understand. In C/C++ programming '++' operator stands for increment of 1. = (((((0!)++)++)++)++)! = (((((1)++)++)++)++)! = (((2++)++)++)! = ((3++)++)! = (4++)! = 5! = 120