111 = 444/4
112 = 44/.4 + √4

113 seems to be quite difficult.

113 = gamma(gamma(4)) - 4 - (√4 / √.4~) ;)
113 = (√4 + (√4 + 4!)%)) / (√4)% (found in a table)

Anyone for a solution without gamma and % ?

Two more "gamma" solutions:

113 = gamma(gamma(4)) - √4 / .4 - √4
113 = (√4 / .4)! - gamma(4) - gamma(√4)

[QUOTE=Andi47;98073]Two more "gamma" solutions[/QUOTE]
Ok, now we now know gamma(gamma(4))=120 and that gamma(4)+gamma(√4)=7
But what is the gamma functiun ?

I did not find an explanation on internet, but I suppose I did not look hard enough.

[QUOTE=S485122;98096]Ok, now we now know gamma(gamma(4))=120 and that gamma(4)+gamma(√4)=7
But what is the gamma functiun ?

I did not find an explanation on internet, but I suppose I did not look hard enough.[/QUOTE]

[URL="http://en.wikipedia.org/wiki/Gamma_function"]Wikipedia:Gamma Function[/URL]

for integers: gamma(n) = (n-1)!

Edit: I did not find any solution for 113 with only +, -, *, /, ^, √, .4 and .4~ in the internt, some pages even belive that this is impossible, although there is now prove for possibility or impossibility. Maybe one of you finds one?

For the record I do NOT have a solution to 113 either.....within my constraints.

114 = (√4 / .4)! - 4 - √4
115 = (√4 / .4)! - (√4 /.4)
116 = (√4 / .4)! - √4 - √4
117 = (√4 / .4)! - √(4/.4~)

118 = (√4 / .4)! - 4 + √4
119 = (√4 / .4)! - 4 / 4
120 = (√4 / .4)! + 4 - 4
121 = (√4 / .4)! + 4 / 4

122 = (√4 / .4)! + 4/ √4
123 = (√4 / .4)! + √(4 /.4~)
124 = (√4 / .4)! + √4 +√4
125 = (√4 / .4)! + √4 / .4

126 = √(√(√(4^4!))) * √4 - √4
127 = √(√(√((√4 / .4)^4!))) + √4
128 = √(√(√(4^4!))) * (4 - √4)
129 = √(√(√((√4 / .4)^4!))) + 4

130 = (√4 / .4)! + 4/.4
131 = ( 4^4 + gamma(4) )/ √4 (Am I throwing in the towel too early?)
132 = (√4 / .4)! + 4!/√4