[quote=cheesehead;102185]218 = 4 * 4! / .4~ + √4
< snip >
220 = 4 * 4! / .4~ + 4[/quote]Lazy me. :blush: There are solutions using more elementary (to me, anyway ~) operations.

[QUOTE=cheesehead;102185]With single gamma:
213 = (4! * gamma(4) - √4) / √.4~[/QUOTE]

Ah, [i]that's[/i] how I got to 144 the first time. Must write things down in future, rather than relying on memory. Of course, I'll probably forget to do that.

220 = 44 * √4 / .4

221 = (gamma(4) / .4) ^ √4 - 4
222 = 444 / √4
223 = (gamma(4) / .4) ^ √4 - √4
224 = (4 + 4) * (4 + 4!)

225 = ((4 + √4) / .4) ^ √4

226 is stumping me at the moment

226 = (gamma(4) / .4)[sup]√4[/sup] + gamma(√4)
227 = (gamma(4) / .4)[sup]√4[/sup] + √4
228 = 4[sup]4[/sup] - 4! - 4
229 = (gamma(4) / .4)[sup]√4[/sup] + 4

With only one gamma:

226 = 4[sup]4[/sup] - 4! - gamma(4)

230 = 4 ^ 4 - 4! - √4
231 = 4 ^ 4 - 4! - gamma(√4)
232 = (4 * 4) ^ √4 - 4!
233 = 4 ^ 4 - 4! + gamma(√4)

I think I'll give up here for now, and see if 'better' (i.e. fewer / no gammas and/or fewer / no %s) solutions are do-able for the smaller numbers.

EDIT:
Actually, cheeky question, could petrw1 do another invaluable 'solutions so far' list, please?

234 = (4 * (√4 + 4!)) / .4~
or 234 = 4[sup]4[/sup] - 4! + √4

235 = (4 * 4! - √4) / .4
236 = 4[sup]4[/sup] - 4! + 4
237 = gamma(gamma(4)) * √4 - √4 / √(.4~)

[quote=cheesehead;102510]234 = 4 ^ 4 - 4! + √4
235 = (4! * 4 - √4) / .4
236 = 4 ^ 4 - 4! + 4[/quote]
Is there an echo in here? :crank:

If you look really hard, there are erasure marks between posts #151 and #152, timestamped a few minutes before this post. :-}

- - -

238 = 4! * 4 / .4 - √4
239 = (4! * 4 - .4) / .4
240 = 4 ^ 4 - 4 * 4
241 = (4! * 4 + .4) / .4

As a famous Genie once said: "Your wish is my command"

Where there are multiple solutions I list all the solutions except, if there are gamma/percent free solutions I list them only but if all solutions contain gamma/percent I list all these solutions even if one has more or less of these....see 113.

I substituted the gamma symbol (an upside down L) for the word gamma.

I proceeded all gamma/percent answers with an asterisk (*).

0 = 4 + 4 - 4 - 4
1 = (4+4)^(4-4) = (4!-4)^(4-4)
2 = 4/4 + 4/4
3 = 4-4^(4-4)
4 = 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-√4
11 = 44/(√4+√4)
12 = 4+4+√(4*4)
13 = 4!-44/4
14 = 4/.4 + √(4*4)
15 = 44/4 + 4 = 4*4 -4/4
16 = 4*4*4/4
17 = 4*4 + 4/4
18 = 44 - 4! - √4
19 = 4! - 4 - 4/4
20 = (44 - 4) / √4
21 = 4! - 4 + 4/4
22 = 44/(4/√4) = 4!-4/(4-√4)
23 = 4!-4^(4-4)
24 = 4!-4+(√4+√4)
25 = 4!+4^(4-4)
26 = 4!+√4 +4-4
27 = 4!+√4 +4/4
28 = 4!+4 +4-4
29 = 4!+4 +4/4
30 = 4!+√4+√4+√4
31 = 4! + 4 / .4~ - √4 = 4! + √4 + √4/.4
32 = 4 ^ √(√4 + √4) * √4
33 = 4! + (√4 + √4) / .4~ = 4! + 4 + √4/.4
34 = 4! + 4 + 4 + √4
35 = (4 * 4 - √4) / .4
36 = ((√4/.4)! + 4!) / 4
37 = (4!+.4)/.4 - 4! = 4! + (4! + √4) / √4 = 4! + 4 + 4 / .4~
38 = 4! + 4 + 4 / .4 = 44 - 4 - √4
39 = 44 - √4 / .4
40 = 44 - √4 - √4
41 = (4*4+.4)/.4
42 = 44 - 4/√4
43 = 44 - 4/4
44 = 44 +4 -4
45 = 44 + 4 / 4
46 = 44 + 4 / √4
47 = 4! + 4! - 4 / 4
48 = 4! + 4! + 4 - 4 = 44 + √4 + √4
49 = (√4/.4 + √4) ^ √4 = 4! + 4! + 4/4
50 = (√4 * 4) / (.4^√4) = √4 * (4! + 4/4)
51 = (4! - √4) /.4 - 4
52 = ((√4 + √4)! + √4) * √4 = (4! + √4) * √4
53 = 44 + 4/.4~ = (4! - √4) /.4 -√4
54 = 4! * √4 + 4 + √4
55 = (44 / √4) /.4
56 = (4 / .4 + 4) * 4
57 = (4! - √4) /.4 +√4
58 = 4! * √4 + 4/.4
59 = (4! -√4) / .4 + 4
60 = 4 * 4 * 4 - 4 = 4^4 / 4 - 4
61 = ((√4 / .4)! + √4) / √4
62 = ((√4 / .4)! + 4) / √4 = (√4 / .4)! / (4 / √4)
63 = (4! + √4) /.4 - √4
64 = 4*4*√4*√4
65 = 4!/.4 + √4/.4
66 = 4 * 4 * 4 + √4
67 = (4! + √4) / .4 + √4
68 = 4 * 4 * 4 + 4
69 = (4! + √4) / .4 + 4
70 = 4! + 4! + 4! - √4
71 = (4! + 4 + .4) / .4
72 = 44 + 4! + 4
73 = ( √4 *4! + √(.4~) ) / √(.4~) = 4/.4~ + √(√(√4))^(4!)
74 = 4/.4 + √(√(√4)^(4!))
75 = (4! + 4 + √4) / .4
76 = √(√(√(4^(4!)))) + 4! / √4
77 = ( √4 / √(.4~))^4 - 4 = (4! + 4!/4) / .4 + √4
78 = (4! / .4~) + (√4 + √4)!
79 = (√4 / √(.4~))^4 - √4
80 = (4 / .4) * (4 + 4)
81 = (4 - 4/4 ) ^ 4
82 = (4! / .4~) + 4! + 4
83 = (√4 / √(.4~))^4 + √4
84 = 44*√4 - 4
85 = (4/.4~)^√4+4
86 = 44*√4 - √4
87 = 4! * 4 - 4 / .4~
88 = 4! * 4 - 4 - 4
89 = (4! / √(.4~) - .4) / .4
90 = 4! * 4 - 4 - √4
91 = (4! / √(.4~) + .4) / .4 = 4! * 4 - √4 / .4
92 = 4*4!-√4-√4
93 = 4! * 4 - √4 / √(.4~)
94 = 4! * 4 - 4 / √4
95 = 4! * 4 - 4 / 4
96 = 4! * 4 - 4 + 4
97 = 4! * 4 + 4 / 4
98 = 4! * 4 + 4 / √4
99 = 44 / √(.4~ * .4~)
100 = (4! + 4/4) * 4 = 4/.4 * 4/.4 = 4!*4*(4/4)
101 = 4! * 4 + √4 / .4
102 = 4! * 4 + 4 + √4
103 = 44 / .4~ + 4
104 = 4! * 4 + 4 + 4
105 = 4*4! + 4/.4~
106 = 4! * 4 + 4/.4
107 = (4! * √4 - .4~) / .4~
108 = 4! *4 + 4! / √4
109 = (4! *√4 + .4~) / .4~
110 = (√4 / .4)! - 4 / .4
111 = 444/4
112 = 44/.4 + √4
*113 = (√4 / .4)! - Γ(4) - Γ(√4) = (√4 + (√4 + 4!)%)) / (√4)% = Γ(Γ(4)) - √4 / .4 - √4 = Γ(Γ(4)) - 4 - (√4 / √.4~)
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) / .4~ - 4
132 = (√4 / .4)! + 4!/√4
133 = (4! / .4) / .4~ -√4
134 = (4! /.4 - .4~) / .4 = 44 / .4 + 4!
135 = ((√4 * √4)! / .4) /.4~
136 = (4! /.4 + .4~) / .4 = (√4/.4)! + 4^√(4)
137 = (4! /.4~) / .4 + √4
138 = (4! * 4 - 4) / √(.4~) = (4! ^ √4 - 4!) / 4
139 = (4! / .4~) / .4 + 4
140 = (4! / √4) ^ (√4) - 4
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
149 = √( √( √( (√4/.4) ^ 4! ) ) ) + 4! = (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
156 = √(√(√(4^4!))) / .4 - 4
*157 = ((4% + √(.4~)) / .4~%) - √4
158 = √(√(√(4^4!))) / .4 - √4
159 = (√(√(√(4^4!)))-.4) / .4
160 = 4 * 4 * 4/.4 = 4^4 - 4!*4
161 = (√(√(√(4^4!)))+.4) / .4
162 = (4 / .4~) ^ √4 * √4
*163 = ((4 + 4!)% + .4~) / .4~% = (Γ(Γ(4))% + √(√(√(4^4!)))) / .4
164 = (√4 / .4)! + 44 = √(√(√(4^4!)))) / .4 + 4
165 = (√4+ √(√(√(4^4!))))) / .4 = 44 / (.4 * √.4~)
166 = 4! * (.4 ^ (-√4) + √.4~)
*167 = Γ(Γ(4)) + 4! * √4 - Γ(√4)
168 = ((√4 / .4~) + 4) * 4!
169 = ((4 / .4~) + 4) ^ √4
170 = (√(√(√(4^4!))) + 4) / .4 = (4! + 44) / .4
*171 = Γ(Γ(4)) / √.4~ - 4/.4~
172 = 44 * 4 - 4
*173 = Γ(Γ(4)) + (4! - .4~)/.4~
174 = 44 * 4 - √4
175 = ((4 + 4!) / .4) / .4
176 = 44 * (√4 + √4)
177 = ((√4 / .4)! - √4) / √.4~
178 = (4 * 44) + √4
179 = ((4 + √4)! - 4) / 4
180 = 4 + (4 * 44)
181 = ((√4 / .4)! + √.4~)/√.4~ = (4 + (4 + √(4))!) / 4
182 = ((4 + √(4))! / 4) + √(4)
183 = (√(4) + (√(4) / .4)!) / √(.4~)
184 = 4 * (√(4) + 44)
*185 = Γ(Γ(4)) + √(√(√(4^4!))) + Γ(√4))
186 = ((√4 / .4)! + 4) / √.4~
*187 = ((Γ(4))! + 4 + 4!) / 4
188 = (4 + 4) * 4! - 4
189 = (4! + 4! / .4) / .4~
190 = (4 + 4) * 4! - √4
*191 = ((Γ(4))! + 44) / 4
192 = (44 + 4) * 4
*193 = (4 + 4) * 4! + Γ(√4)
194 = (4 + 4) * 4! + √4
195 = (4! + (4! / .4~)) / .4
196 = (4! / √4 + √4) ^ √4
*197 = (4 - (4 + √4)%) / √4%
198 = (44 * √4) / .4~
*199 = (4 + 4) / 4% - Γ(√4)
200 = 44 * 4 + 4!
*201 = (4 + 4) / 4% + Γ(√4)
202 = 4^4 - ( 4! / .4~ )
*203 = Γ(Γ(4)) / √.4~ + 4! - Γ(√4)
204 = (√4 / .4)! / √.4~ + 4!
*205 = Γ(Γ(4)) / √.4~ + 4! + Γ(4)
*206 = Γ(Γ(4)) / √.4~ + 4! + √4
*207 = (4! * Γ(4) - Γ(4)) / √.4~
208 = 4 ^ 4 - 4! - 4!
*209 = ((Γ(4) + Γ(√(4)))! - 4!) / 4!
210 = (4! + 4! / .4) / .4
*211 = (Γ(4 + 4) + 4!) / 4!
212 = 4 ^ 4 - 44
*213 = (4! * Γ(4) - √4) / √.4~ = (Γ(Γ(4)) + 4! - √4) / √.4~
214 = 4 * 4! / .4~ - √4
215 = ((4 * 4!) - .4~) / .4~
216 = 4! * (4 + 4) + 4!
217 = (4 * 4! + .4~) / .4~
218 = 4 * 4! / .4~ + √4
*219 = (4! * Γ(4) + √4) / √.4~
220 = 4 * 4! / .4~ + 4 = 44 * √4 / .4
*221 = (Γ(4) / .4) ^ √4 - 4
222 = 444 / √4
*223 = (Γ(4) / .4) ^ √4 - √4
224 = (4 + 4) * (4 + 4!)
225 = ((4 + √4) / .4) ^ √4
*226 = (Γ(4) / .4)√4 + Γ(√4) = 44 - 4! - Γ(4)
*227 = (Γ(4) / .4)√4 + √4
228 = 44 - 4! - 4
*229 = (Γ(4) / .4)√4 + 4
230 = 4 ^ 4 - 4! - √4
*231 = 4 ^ 4 - 4! - Γ(√4)
232 = (4 * 4) ^ √4 - 4!
*233 = 4 ^ 4 - 4! + Γ(√4)