[quote=petrw1;98248]NOT VALID: (√4).4 = 2.4, (√4).4~ = 2.4~[/quote]Concatenation isn't necessary anyway for those particular examples (Addition can be used: √4 + .4 = 2.4, √4 + .4~ = 2.4~), but there's no such easy get-around in the following examples:

.√4 = .2 (concatenation of "." with "√4" to produce, in effect, division by 10 after square-root)

4(4!) = 424 (concatenation of "4!" to produce, in effect, multiplication of the first "4" by 100)

- - - - -

[quote=Andi47]138 = (4! * 4 - 4) / √(.4~)[/quote]or, without "." or "~":

138 = (4! ^ √4 - 4!) / 4

[QUOTE=Andi47;98267]Nobody for 141? It is possible without gamma and %...

(I could post it, but I already had my 4 solutions this turn.)[/QUOTE]

Hint: 94 - .6~

141 = (4! * 4 - √4)/ √(.4~)
142 = 4! * 4! /4 - √4
143 = (4! *4! -4) /4
144 = 4! *4! /√4 /√4

145 = (4! ^ √4 + 4) / 4
146 = (4! / √4) ^ √4 + √4
147 = (4! * 4 + √4) / √.4~
148 = (4! / √4) ^ √4 + 4

[quote]100 = 4/.4 * 4/.4[/quote]... or, pointlessly,

100 = (4! + 4/4) * 4

- - -

149 = √( √( √( (√4/.4) ^ 4! ) ) ) + 4!
150 = (4! * 4! + 4!) / 4

151 = (4! / .4 + .4)/.4
152 = (4! / .4) / .4 + √4
153 = (√(√(√(4^4!))) + 4) / .4~
154 = (4! / .4) / .4 + 4

155 = ((4! / .4) + √4)/ .4

[QUOTE=cheesehead;98412]... or, pointlessly,

100 = (4! + 4/4) * 4

- - -

149 = √( √( √( (√4/.4) ^ 4! ) ) ) + 4!
150 = (4! * 4! + 4!) / 4[/QUOTE]

Very inventive answer to 149.
I have:
149 = (4!/.4-.4)/.4

[QUOTE=petrw1;98105]For the record I do NOT have a solution to 113 either.....within my constraints.[/QUOTE]

Interestingly 113 is simply 7 squared + 8 squared. The trouble is, how do you make 7 without using all the 4's?

The list so far ...
 

0 = 4 + 4 - 4 - 4
1 = (4+4)^(4-4)
1 = (4!-4)^(4-4)
2 = 4/4 + 4/4
3 = 4-4^(4-4)
3 = 4-4^(4-4)
4 = 4*4^(4-4)
5 = 4+4^(4-4)
5 = 4+4^(4-4)
6 = 4 + ((4 + 4) / 4)
7 = 4 + 4 - (4 / 4)
8 = 4 * 4 - 4 - 4
9 = 4 + 4 + (4 / 4)
10 = 4*4-4-v4
11 = 44/(v4+v4)
12 = 4+4+v(4*4)
13 = 4!-44/4
14 = 4/.4 + v(4*4)
15 = 44/4 + 4 4*4 -4/4
16 = 4*4*4/4
17 = 4*4 + 4/4
18 = 44 - 4! - v4
19 = 4! - 4 - 4/4
20 = (44 - 4) / v4
21 = 4! - 4 + 4/4
22 = 44/(4/v4) 4!-4/(4-v4)
23 = 4!-4^(4-4)
24 = 4!-4+(v4+v4)
25 = 4!+4^(4-4)
26 = 4!+v4 +4-4
27 = 4!+v4 +4/4
28 = 4!+4 +4-4
29 = 4!+4 +4/4
30 = 4!+v4+v4+v4
31 = 4! + 4 / .4~ - v4
31 = 4! + v4 + v4/.4
32 = 4 ^ v(v4 + v4) * v4
33 = 4! + (v4 + v4) / .4~
33 = 4! + 4 + v4/.4
34 = 4! + 4 + 4 + v4
35 = (4 * 4 - v4) / .4
36 = ((v4/.4)! + 4!) / 4
37 = (4!+.4)/.4 - 4!
37 = (4!+.4)/.4 - 4!
37 = 4! + (4! + v4) / v4
37 = 4! + 4 + 4 / .4~
37 = 4! + 4 + 4 / .4~
38 = 4! + 4 + 4 / .4 44 - 4 - v4
39 = 44 - v4 / .4
40 = 44 - v4 - v4
41 = (4*4+.4)/.4
42 = 44 - 4/v4
43 = 44 - 4/4
44 = 44 +4 -4
45 = 44 + 4 / 4
46 = 44 + 4 / v4
47 = 4! + 4! - 4 / 4
48 = 4! + 4! + 4 - 4 44 + v4 + v4
49 = (v4/.4 + v4) ^ v4
49 = 4! + 4! + 4/4
50 = (v4 * 4) / (.4^v4)
50 = v4 * (4! + 4/4)
51 = (4! - v4) /.4 - 4
52 = ((v4 + v4)! + v4) * v4
52 = ((v4 + v4)! + v4) * v4
52 = (4! + v4) * v4
53 = 44 + 4/.4~ (4! - v4) /.4 -v4
54 = 4! * v4 + 4 + v4
55 = (44 / v4) /.4
56 = (4 / .4 + 4) * 4
57 = (4! - v4) /.4 +v4
58 = 4! * v4 + 4/.4
59 = (4! -v4) / .4 + 4
60 = 4 * 4 * 4 - 4 4^4 / 4 - 4
61 = ((v4 / .4)! + v4) / v4
62 = ((v4 / .4)! + 4) / v4
62 = (v4 / .4)! / (4 / v4)
62 = (v4 / .4)! / (4 / v4)
63 = (4! + v4) /.4 - v4
64 = ... mmm so many ways ...
65 = 4!/.4 + v4/.4
66 = 4 * 4 * 4 + v4
67 = (4! + v4) / .4 + v4
68 = 4 * 4 * 4 + 4
69 = (4! + v4) / .4 + 4
70 = 4! + 4! + 4! - v4
71 = (4! + 4 + .4) / .4
72 = 44 + 4! + 4
73 = ( v4 *4! + v(.4~) ) / v(.4~)
73 = 4/.4~ + v(v(v4))^(4!)
74 = 4/.4 + v(v(v4)^(4!))
75 = (4! + 4 + v4) / .4
76 = v(v(v(4^(4!)))) + 4! / v4
77 = ( v4 / v(.4~))^4 - 4
77 = (4! + 4!/4) / .4 + v4
77 = (4! + 4!/4) / .4 + v4
78 = (4! / .4~) + (v4 + v4)!
79 = (v4 / v(.4~))^4 - v4
80 = (4 / .4) * (4 + 4)
81 = (4 - 4/4 ) ^ 4
82 = (4! / .4~) + 4! + 4
83 = (v4 / v(.4~))^4 + v4
84 = 44*v4 - 4
85 = (4/.4~)^v4+4
86 = 44*v4 - v4
87 = 4! * 4 - 4 / .4~
88 = 4! * 4 - 4 - 4
89 = (4! / v(.4~) - .4) / .4
90 = 4! * 4 - 4 - v4
91 = (4! / v(.4~) + .4) / .4
91 = 4! * 4 - v4 / .4
92 = 4*4!-v4-v4
93 = 4! * 4 - v4 / v(.4~)
94 = 4! * 4 - 4 / v4
95 = 4! * 4 - 4 / 4
96 = 4! * 4 - 4 + 4
97 = 4! * 4 + 4 / 4
98 = 4! * 4 + 4 / v4
99 = 44 / v(.4~ * .4~)
100 = (4! + 4/4) * 4
100 = (4! + 4/4) * 4
100 = 4/.4 * 4/.4
100 = 4/.4 * 4/.4
100 = 4!*4*(4/4)
101 = 4! * 4 + v4 / .4
102 = 4! * 4 + 4 + v4
103 = 44 / .4~ + 4
104 = 4! * 4 + 4 + 4
105 = 4*4! + 4/.4~
106 = 4! * 4 + 4/.4
107 = (4! * v4 - .4~) / .4~
108 = 4! *4 + 4! / v4
109 = (4! *v4 + .4~) / .4~
110 = (v4 / .4)! - 4 / .4
111 = 444/4
112 = 44/.4 + v4
113 = seems to be quite difficult.
114 = (v4 / .4)! - 4 - v4
115 = (v4 / .4)! - (v4 /.4)
116 = (v4 / .4)! - v4 - v4
117 = (v4 / .4)! - v(4/.4~)
118 = (v4 / .4)! - 4 + v4
119 = (v4 / .4)! - 4 / 4
120 = (v4 / .4)! + 4 - 4
121 = (v4 / .4)! + 4 / 4
122 = (v4 / .4)! + 4/ v4
123 = (v4 / .4)! + v(4 /.4~)
124 = (v4 / .4)! + v4 +v4
125 = (v4 / .4)! + v4 / .4
126 = v(v(v(4^4!))) * v4 - v4
127 = v(v(v((v4 / .4)^4!))) + v4
128 = v(v(v(4^4!))) * (4 - v4)
129 = v(v(v((v4 / .4)^4!))) + 4
130 = (v4 / .4)! + 4/.4
130 = (v4 / .4)! + 4/.4
131 = (4! / .4) / .4~ - 4
132 = (v4 / .4)! + 4!/v4
132 = (v4 / .4)! + 4!/v4
133 = (4! / .4) / .4~ -v4
134 = (4! /.4 - .4~) / .4 44 / .4 + 4!
135 = ((v4 * v4)! / .4) /.4~
136 = (4! /.4 + .4~) / .4 (sqrt(4)/.4)! + 4^sqrt(4)
137 = (4! /.4 ) / .4 + sqrt(4)
137 = (4! /.4~) / .4 + v4
138 = (4! * 4 - 4) / v(.4~)
138 = (4! * 4 - 4) / v(.4~)
138 = (4! ^ v4 - 4!) / 4
139 = (4! / .4~) / .4 + 4
140 = (4! / v4) ^ (v4) - 4
141 = (4! * 4 - v4)/ v(.4~)
142 = 4! * 4! /4 - v4
143 = (4! *4! -4) /4
144 = 4! *4! /v4 /v4
145 = (4! ^ v4 + 4) / 4
146 = (4! / v4) ^ v4 + v4
147 = (4! * 4 + v4) / v.4~
148 = (4! / v4) ^ v4 + 4
149 = (4!/.4-.4)/.4
149 = v( v( v( (v4/.4) ^ 4! ) ) ) + 4!
149 = v( v( v( (v4/.4) ^ 4! ) ) ) + 4!
150 = (4! * 4! + 4!) / 4
150 = (4! * 4! + 4!) / 4
151 = (4! / .4 + .4)/.4
152 = (4! / .4) / .4 + v4
153 = (v(v(v(4^4!))) + 4) / .4~
154 = (4! / .4) / .4 + 4
155 = ((4! / .4) + v4)/ .4

156 = √(√(√(4^4!))) / .4 - 4
157 = (gamma(4)! + 4) / 4 - 4! (anyone for a gamma-free solution?)