4444

micronesia

United States24604 Posts

August 27 2008 03:06 GMT

In celebration of my 4444th post I present you with a math problem:

Given no more than four instances of the digit 4,
represent all integers using a finite number of
mathematical symbols and operators in common use.

The first person to represent the solution for integers 1-1000 wins (and probably sucks at math).

Rules edit: Use a spoiler :<

Edit: apparently this OP counted as a post but np

Bonus:

On August 27 2008 12:40 Caller wrote:
fuck you micro

i'm not going to answer your question because 4444 means death death death death in chinese thats really unlucky

curse you micro for being a provincial physics teacher

kpcrew

Korea (South)1071 Posts

August 27 2008 03:15 GMT

well i guess i could think of some but i dont want to go into detail -_-
1000 is alot

micronesia

United States24604 Posts

August 27 2008 03:16 GMT

On August 27 2008 12:15 kpcrew(Gg) wrote:
well i guess i could think of some but i dont want to go into detail -_-
1000 is alot

Think outside the box lol.

Jonoman92

United States9102 Posts

August 27 2008 03:16 GMT

Congrats on 4444 but I have no clue how to solve that problem.

kpcrew

Korea (South)1071 Posts

August 27 2008 03:17 GMT

u mean like 4/4 = 1 4+4/4 = 2 4+4+4/4 =3 4=4 etc?

kpcrew

Korea (South)1071 Posts

August 27 2008 03:19 GMT

:sigh: 4^4*4 is 1024

micronesia

United States24604 Posts

August 27 2008 03:19 GMT

On August 27 2008 12:17 kpcrew(Gg) wrote:
u mean like 4/4 = 1 4+4/4 = 2 4+4+4/4 =3 4=4 etc?

Yeah using 4 and symbols.

AcrossFiveJulys

United States3612 Posts

August 27 2008 03:24 GMT

"Given no more than four instances of the digit 4,
represent all integers using a finite number of
mathematical symbols and operators in common use."

Can you clarify? This makes it sound like I can "represent" all integers without using 4 at all by always replacing each 4 in each integer by "X", thus we have represented all integers... I don't think that's what you intended.

Polemarch

Canada1564 Posts

August 27 2008 03:31 GMT

+ Show Spoiler +

Uh just write the numbers down? None of the numbers 1-1000 have more than four 4's

FakeSteve[TPR]

Valhalla18444 Posts

August 27 2008 03:31 GMT

#10

huh? represent every number from 1 to 1000?

how about 4X/4? that's every single number ever

Caller

Poland8075 Posts

August 27 2008 03:40 GMT

#11

fuck you micro

i'm not going to answer your question because 4444 means death death death death in chinese thats really unlucky

curse you micro for being a provincial physics teacher

micronesia

United States24604 Posts

August 27 2008 03:41 GMT

#12

On August 27 2008 12:24 AcrossFiveJulys wrote:
"Given no more than four instances of the digit 4,
represent all integers using a finite number of
mathematical symbols and operators in common use."

Can you clarify? This makes it sound like I can "represent" all integers without using 4 at all by always replacing each 4 in each integer by "X", thus we have represented all integers... I don't think that's what you intended.

On August 27 2008 12:31 Polemarch wrote:
+ Show Spoiler +

Uh just write the numbers down? None of the numbers 1-1000 have more than four 4's

On August 27 2008 12:31 FakeSteve[TPR] wrote:
huh? represent every number from 1 to 1000?

how about 4X/4? that's every single number ever

Yeah the question isn't 100% clear. It means only using the digit 4 (up to four times) and mathematical operators/symbols. I guess using x is technically within constraints, but I do not wish for that.

BottleAbuser

Korea (South)1888 Posts

August 27 2008 03:43 GMT

#13

My guess:

+ Show Spoiler +

You could vastly increase the number of numbers representable by using different bases, perhaps all of them. Although if you have to explicitly state the base, that wouldn't work so well.

stanley_

United States816 Posts

August 27 2008 03:45 GMT

#14

how do you make the enigma sign or that weird E?

GoldenSun

21 Posts

August 27 2008 03:47 GMT

#15

i had this problem a while back in calculus class
+ Show Spoiler +

$[image loading]$

from wikipedia http://en.wikipedia.org/wiki/Four_fours

BottleAbuser

Korea (South)1888 Posts

August 27 2008 03:51 GMT

#16

GoldenSun wins the thread.

micronesia

United States24604 Posts

August 27 2008 03:54 GMT

#17

On August 27 2008 12:51 BottleAbuser wrote:
GoldenSun wins the thread.

Agreed. I wasn't even aware of a general formulation. I was expecting a copy/paste from another source to win, but I'm forced to accept GoldenSun's answer... even though I'm not 100% happy with the way you have to express the quantity of square routes using such a crude method.

EtherealDeath

United States8366 Posts

August 27 2008 03:57 GMT

#18

I like how you have gained 8 more posts since 4444 -_-

29 fps

United States5720 Posts

August 27 2008 03:57 GMT

#19

he cited his source, so he did copy paste...

micronesia

United States24604 Posts

August 27 2008 04:01 GMT

#20

On August 27 2008 12:57 EtherealDeath wrote:
I like how you have gained 8 more posts since 4444 -_-

I guess you were too slow.

On August 27 2008 12:57 29 fps wrote:
he cited his source, so he did copy paste...

I meant a copy/paste of 1000 lines of answers (which is very easy to do).

LiAlH4

New Zealand111 Posts

August 27 2008 04:05 GMT

#21

+ Show Spoiler +

(4-4)/(4-4)

micronesia

United States24604 Posts

August 27 2008 04:08 GMT

#22

On August 27 2008 13:05 LiAlH4 wrote:
+ Show Spoiler +

(4-4)/(4-4)

Undefined. Not valid.

thunk

United States6233 Posts

August 27 2008 05:56 GMT

#23

I'll do it, it was just a google away.

+ Show Spoiler +

http://www.dwheeler.com/fourfours/fourfours.txt
The website actually goes up to like 40,000.
0 (0) = 44-44
1 (0) = 44/44
2 (0) = 4/4+4/4
3 (0) = (4+4+4)/4
4 (0) = 4*(4-4)+4
5 (0) = (4*4+4)/4
6 (0) = 4*.4+4.4
7 (0) = 44/4-4
8 (0) = 4+4.4-.4
9 (0) = 4/4+4+4
10 (0) = 44/4.4
11 (0) = 4/.4+4/4
12 (0) = (44+4)/4
13 (0) = 4!-44/4
14 (0) = 4*(4-.4)-.4
15 (0) = 44/4+4
16 (0) = .4*(44-4)
17 (0) = 4/4+4*4
18 (0) = 44*.4+.4
19 (0) = 4!-4-4/4
20 (0) = 4*(4/4+4)
21 (0) = (4.4+4)/.4
22 (0) = 44*sqrt(4)/4
23 (0) = (4*4!-4)/4
24 (0) = 4*4+4+4
25 (0) = (4*4!+4)/4
26 (0) = 4/.4+4*4
27 (0) = 4-4/4+4!
28 (0) = 44-4*4
29 (0) = 4/.4/.4+4
30 (0) = (4+4+4)/.4
31 (0) = (4!+4)/4+4!
32 (0) = 4*4+4*4
33 (0) = (4-.4)/.4+4!
34 (0) = 44-4/.4
35 (0) = 44/4+4!
36 (0) = 44-4-4
37 (0) = (sqrt(4)+4!)/sqrt(4)+4!
38 (0) = 44-4!/4
39 (0) = (4*4-.4)/.4
40 (0) = 44-sqrt(4*4)
41 (0) = (sqrt(4)+4!)/.4-4!
42 (0) = sqrt(4)+44-4
43 (0) = 44-4/4
44 (0) = 44.4-.4
45 (0) = 4/4+44
46 (0) = 44-sqrt(4)+4
47 (0) = 4!+4!-4/4
48 (0) = 4*(4+4+4)
49 (0) = (4!-4.4)/.4
50 (0) = 4!/4+44
51 (0) = (4!-sqrt(4))/.4-4
52 (0) = 4+4+44
53 (0) = sqrt(4)/.4+4!+4!
54 (0) = 4/.4+44
55 (0) = 44/(.4+.4)
56 (0) = 4*(4/.4+4)
57 (0) = (4!-.4)/.4-sqrt(4)
58 (0) = (4^4-4!)/4
59 (0) = 4!/.4-4/4
60 (0) = 4*4+44
61 (0) = 4!/.4+4/4
62 (0) = (.4+.4+4!)/.4
63 (0) = (4^4-4)/4
64 (0) = 4!-4+44
65 (0) = (4^4+4)/4
66 (0) = (4!+4)/.4-4
67 (0) = (sqrt(4)+4!)/.4+sqrt(4)
68 (0) = 4*4*4+4
69 (0) = (4-.4+4!)/.4
70 (0) = 4!/.4+4/.4
71 (0) = (4!+4.4)/.4
72 (0) = 4!+44+4
73 (2) = sqrt(sqrt(sqrt(4)^4!))+4/.4~
74 (0) = (4!+4)/.4+4
75 (0) = 4!/(.4+.4)/.4
76 (0) = 4!/.4+4*4
77 (2) = sqrt(4/.4~)^4-4
78 (0) = 4*(4!-4)-sqrt(4)
79 (0) = (4!-sqrt(4))/.4+4!
80 (0) = 4*(4*4+4)
81 (0) = (4/4-4)^4
82 (0) = 4*(4!-4)+sqrt(4)
83 (0) = (4!-.4)/.4+4!
84 (0) = 44*sqrt(4)-4
85 (0) = (4/.4+4!)/.4
86 (0) = 44/.4-4!
87 (2) = 4*4!-4/.4~
88 (0) = 44+44
89 (0) = (sqrt(4)+4!)/.4+4!
90 (0) = 44*sqrt(4)+sqrt(4)
91 (0) = 4*4!-sqrt(4)/.4
92 (0) = 44*sqrt(4)+4
93 (2) = 4*4!-sqrt(4/.4~)
94 (0) = 4*(4!-.4)-.4
95 (0) = 4*4!-4/4
96 (0) = 4*(4.4-.4)!
97 (0) = 4*4!+4/4
98 (0) = 4*(4!+.4)+.4
99 (2) = 44/sqrt(.4~*.4~)
100 (0) = 44/.44
101 (0) = sqrt(4)/.4+4*4!
102 (0) = .4*4^4-.4
103 (2) = 44/.4~+4
104 (0) = 4!/.4+44
105 (0) = (44-sqrt(4))/.4
106 (0) = 44/.4-4
107 (2) = (4!+4!-.4~)/.4~
108 (0) = 44/.4-sqrt(4)
109 (0) = (44-.4)/.4
110 (0) = 44/sqrt(.4*.4)
111 (0) = 444/4
112 (0) = sqrt(4)+44/.4
113 (4) = gamma(gamma(4))-(4!+4)/4
114 (0) = 44/.4+4
115 (0) = (sqrt(4)+44)/.4
116 (0) = (4/4+4)!-4
117 (2) = (4!+4!+4)/.4~
118 (0) = (4/4+4)!-sqrt(4)
119 (0) = (4!+4!-.4)/.4
120 (0) = (44+4)/.4
121 (0) = sqrt(44/4)^4
122 (0) = (4/4+4)!+sqrt(4)
123 (0) = sqrt(sqrt(sqrt((sqrt(4)/.4)^4!)))-sqrt(4)
124 (0) = (4/4+4)!+4
125 (0) = (4!-4)/.4/.4
126 (0) = (4^4-4)/sqrt(4)
127 (0) = (4^4-sqrt(4))/sqrt(4)
128 (0) = 4*4*(4+4)
129 (0) = (sqrt(4)+4^4)/sqrt(4)
130 (0) = (4^4+4)/sqrt(4)
131 (2) = 4!/.4/.4~-4
132 (0) = 4^4/sqrt(4)+4
133 (2) = 4!/.4/.4~-sqrt(4)
134 (0) = 44/.4+4!
135 (2) = sqrt(4*4)!/.4~/.4
136 (0) = 4*(4/.4+4!)
137 (2) = 4!/.4/.4~+sqrt(4)
138 (0) = (4!*4!-4!)/4
139 (2) = 4!/.4/.4~+4
140 (0) = 4*4!+44
141 (2) = (4*4!-sqrt(4))/sqrt(.4~)
142 (0) = 4!*4!/4-sqrt(4)
143 (0) = (4!*4!-4)/4
144 (0) = 4!*(4/.4-4)
145 (0) = (4!*4!+4)/4
146 (0) = 4!/.4/.4-4
147 (2) = (4*4!+sqrt(4))/sqrt(.4~)
148 (0) = 4!*4!/4+4
149 (0) = (4!/.4-.4)/.4
150 (0) = sqrt(4*4)!/.4/.4
151 (0) = (4!/.4+.4)/.4
152 (0) = 4*44-4!
153 (2) = (4!+44)/.4~
154 (0) = 4!/.4/.4+4
155 (0) = (4!/.4+sqrt(4))/.4
156 (0) = 4!/.4+4*4!
157 (4) = (gamma(4)!+4)/4-4!
158 (0) = sqrt(sqrt(sqrt(4)^4!))/.4-sqrt(4)
159 (0) = (sqrt(sqrt(sqrt(4)^4!))-.4)/.4
160 (0) = 4*(44-4)
161 (0) = (sqrt(sqrt(sqrt(4)^4!))+.4)/.4
162 (0) = sqrt(sqrt(sqrt(4)^4!))/.4+sqrt(4)
163 (4) = gamma(gamma(4))-gamma(sqrt(4))+44
164 (0) = (sqrt(4)/.4)!+44
165 (0) = (sqrt(sqrt(sqrt(4)^4!))+sqrt(4))/.4
166 (4) = gamma(4)!/4.4~+4
167 (4) = gamma(4)*(4!+4)-gamma(sqrt(4))
168 (0) = 4*(44-sqrt(4))
169 (0) = (sqrt(4)+4!)^sqrt(4)/4
170 (0) = (4!+44)/.4
171 (4) = (gamma(gamma(4))-44)/.4~
172 (0) = 4*44-4
173 (4) = (gamma(4)!-4!-4)/4
174 (0) = 4*44-sqrt(4)
175 (0) = (4!+4)/.4/.4
176 (0) = 44*sqrt(4*4)
177 (2) = ((sqrt(4)/.4)!-sqrt(4))/sqrt(.4~)
178 (0) = sqrt(4)+4*44
179 (0) = ((4!/4)!-4)/4
180 (0) = 4*44+4
181 (0) = ((4!/4)!+4)/4
182 (0) = (4!/4)!/4+sqrt(4)
183 (2) = ((sqrt(4)/.4)!+sqrt(4))/sqrt(.4~)
184 (0) = 4*(sqrt(4)+44)
185 (4) = (gamma(4)!+4)/4+4
186 (0) = ((4!/4)!+4!)/4
187 (4) = (gamma(4)!+4!+4)/4
188 (0) = 4!*(4+4)-4
189 (2) = (4!/.4+4!)/.4~
190 (0) = 4!*(4+4)-sqrt(4)
191 (4) = (gamma(4)!+44)/4
192 (0) = 4*(44+4)
193 (4) = 4!*(4+4)+gamma(sqrt(4))
194 (0) = 4!*(4+4)+sqrt(4)
195 (2) = (4!/.4~+4!)/.4
196 (0) = 4!*(4+4)+4
197 (6) = (square(4!+4)+4)/4
198 (2) = 44*sqrt(4)/.4~
199 (4) = gamma(4)!/(4-.4)-gamma(sqrt(4))
200 (0) = 4*44+4!
201 (4) = (gamma(4)/.4)^sqrt(4)-4!
202 (2) = 4^4-4!/.4~
203 (4) = (gamma(4)!-4)/4+4!
204 (0) = (4!/4)!/4+4!
205 (4) = (gamma(4)!+4)/4+4!
206 (4) = gamma(4+4)/4!-4
207 (2) = (4*4!-4)/.4~
208 (0) = 4^4-4!-4!
209 (4) = (gamma(4+4)-4!)/4!
210 (0) = (4!/.4+4!)/.4
211 (4) = (gamma(4+4)+4!)/4!
212 (0) = 4^4-44
213 (4) = (4!*gamma(4)-sqrt(4))/sqrt(.4~)
214 (0) = sqrt(sqrt(sqrt((4!/4)^4!)))-sqrt(4)
215 (4) = sqrt(gamma(4)^gamma(4))-4/4
216 (0) = 4!*(4-.4)/.4
217 (2) = (4*4!+.4~)/.4~
218 (0) = sqrt(sqrt(sqrt((4!/4)^4!)))+sqrt(4)
219 (3) = root(.4,4/.4~)-4!
220 (0) = 44*sqrt(4)/.4
221 (4) = (gamma(4)/.4)^sqrt(4)-4
222 (0) = 444/sqrt(4)
223 (4) = (gamma(4)/.4)^sqrt(4)-sqrt(4)
224 (0) = 4*(4!/.4-4)
225 (0) = (4!/4/.4)^sqrt(4)
226 (4) = 4^4-gamma(4)-4!
227 (4) = (gamma(4)/.4)^sqrt(4)+sqrt(4)
228 (0) = 4^4-4-4!
229 (4) = (gamma(4)/.4)^sqrt(4)+4
230 (0) = (4*4!-4)/.4
231 (4) = 4^4-gamma(sqrt(4))-4!
232 (0) = .4*(4!*4!+4)
233 (4) = gamma(sqrt(4))+4^4-4!
234 (0) = sqrt(4)-4!+4^4
235 (0) = (4*4!-sqrt(4))/.4
236 (0) = 4-4!+4^4
237 (4) = root(.4,4/.4~)-gamma(4)
238 (0) = 4*4!/.4-sqrt(4)
239 (3) = root(.4,4/.4~)-4
240 (0) = 4^4-4*4
241 (0) = (4*4!+.4)/.4
242 (0) = 4*4!/.4+sqrt(4)
243 (2) = 4!*sqrt(4/.4~^4)
244 (0) = 4*4!/.4+4
245 (0) = (4*4!+sqrt(4))/.4
246 (0) = 4^4-4/.4
247 (2) = 4^4-4/.4~
248 (0) = 4^4-4-4
249 (4) = root(.4,4/.4~)+gamma(4)
250 (0) = 4^4-4!/4
251 (0) = 4^4-sqrt(4)/.4
252 (0) = sqrt(4*4)^4-4
253 (2) = 4^4-sqrt(4/.4~)
254 (0) = sqrt(4)+4^4-4
255 (0) = 4^4-4/4
256 (0) = 4^(4.4-.4)
257 (0) = 4^4+4/4
258 (0) = 4-sqrt(4)+4^4
259 (2) = sqrt(4/.4~)+4^4
260 (0) = sqrt(4*4)^4+4
261 (0) = sqrt(4)/.4+4^4
262 (0) = 4!/4+4^4
263 (4) = 44*gamma(4)-gamma(sqrt(4))
264 (0) = 4^4+4+4
265 (2) = 4/.4~+4^4
266 (0) = 4^4+4/.4
267 (3) = root(.4,4/.4~)+4!
268 (0) = 4!/sqrt(4)+4^4
269 (2) = ((sqrt(4)/.4)!-.4~)/.4~
270 (2) = (4/4+4)!/.4~
271 (2) = ((sqrt(4)/.4)!+.4~)/.4~
272 (0) = 4^4+4*4
273 (4) = .4*gamma(4)!-gamma(4)/.4
274 (2) = (sqrt(4)/.4)!/.4~+4
275 (0) = 44/.4/.4
276 (0) = 4!-4+4^4
277 (4) = (gamma(gamma(4))+.4)/.4-4!
278 (0) = 4!-sqrt(4)+4^4
279 (2) = ((sqrt(4)/.4)!+4)/.4~
280 (0) = 4*(4!+4)/.4
281 (4) = gamma(sqrt(4))+4^4+4!
282 (0) = sqrt(4)+4^4+4!
283 (4) = (gamma(gamma(4))+4)/.4~+4
284 (0) = 4!+4+4^4
285 (4) = (gamma(gamma(4))-4!/4)/.4
286 (0) = (4!*4!-4)/sqrt(4)
287 (0) = (4!*4!-sqrt(4))/sqrt(4)
288 (0) = 4!*(4+4+4)
289 (0) = (4!*4!+sqrt(4))/sqrt(4)
290 (0) = ((sqrt(4)/.4)!-4)/.4
291 (4) = (gamma(gamma(4))-4+.4)/.4
292 (0) = .4*(4!/4)!+4
293 (4) = .4*gamma(4)!+sqrt(4)/.4
294 (2) = (sqrt(4)/.4)!/.4~+4!
295 (0) = ((sqrt(4)/.4)!-sqrt(4))/.4
296 (0) = (sqrt(4)/.4)!/.4-4
297 (4) = (gamma(gamma(4))+.4)/.4-4
298 (0) = (sqrt(4)/.4)!/.4-sqrt(4)
299 (4) = gamma(gamma(4))/.4-4/4
300 (0) = 4^4+44
301 (0) = ((sqrt(4)/.4)!+.4)/.4
302 (0) = (sqrt(4)/.4)!/.4+sqrt(4)
303 (4) = .4*gamma(4)!+gamma(4)/.4
304 (0) = 4!+4!+4^4
305 (0) = ((sqrt(4)/.4)!+sqrt(4))/.4
306 (4) = (gamma(gamma(4))+4)/.4-4
307 (4) = (gamma(gamma(4))+.4)/.4+gamma(4)
308 (4) = gamma(gamma(4))/.4+4+4
309 (4) = gamma(gamma(4))/.4+4/.4~
310 (0) = ((sqrt(4)/.4)!+4)/.4
311 (4) = (gamma(gamma(4))+4.4)/.4
312 (0) = .4*(4!/4)!+4!
313 (4) = (gamma(gamma(4))+gamma(4))/.4-sqrt(4)
314 (4) = gamma(gamma(4))/.4~+44
315 (4) = gamma(4+4)/4/4
316 (0) = 4!/.4+4^4
317 (4) = (gamma(gamma(4))+gamma(4))/.4+sqrt(4)
318 (2) = .4~*(4!/4)!-sqrt(4)
319 (4) = .4~*gamma(4)!-4/4
320 (0) = 4^4/(.4+.4)
321 (4) = .4~*gamma(4)!+4/4
322 (2) = .4~*(4!/4)!+sqrt(4)
323 (4) = (gamma(4)^4-4)/4
324 (0) = (4!/4)^4/4
325 (0) = (sqrt(4)+4!)!/4!!/sqrt(4)
326 (4) = gamma(4)^4/4+sqrt(4)
327 (4) = gamma(sqrt(4))+gamma(4)+.4~*gamma(4)!
328 (4) = gamma(4)^4/4+4
329 (4) = .4~*gamma(4)!+4/.4~
330 (4) = (gamma(4)^4+4!)/4
331 (4) = sqrt(gamma(sqrt(4))+gamma(gamma(4)))+.4~*gamma(4)!
332 (4) = .4*gamma(4)!+44
333 (4) = (4!*gamma(4)+4)/.4~
334 (4) = (gamma(gamma(4))+4)/.4+4!
335 (4) = .4~*gamma(4)!+gamma(4)/.4
336 (0) = 4!*(4/.4+4)
337 (4) = (gamma(4)!+sqrt(4))/sqrt(4)-4!
338 (0) = sqrt((sqrt(4)+4!)^4/4)
339 (4) = (gamma(gamma(4))+gamma(4))/.4+4!
340 (4) = (gamma(gamma(4))+4*4)/.4
341 (4) = sqrt((gamma(sqrt(4))+gamma(4))^gamma(4))-sqrt(4)
342 (4) = (gamma(gamma(4))+root(.4,4))/.4~
343 (4) = sqrt(((4!+4)/4)^gamma(4))
344 (2) = .4~*(4!/4)!+4!
345 (4) = (4!*gamma(4)-gamma(4))/.4
346 (4) = (gamma(4)!-4!-4)/sqrt(4)
347 (4) = (gamma(4)!-4!-sqrt(4))/sqrt(4)
348 (0) = ((4!/4)!-4!)/sqrt(4)
349 (4) = (gamma(4)!+sqrt(4)-4!)/sqrt(4)
350 (4) = (4!*gamma(4)-4)/.4
351 (4) = (gamma(4)!/4-4!)/.4~
352 (0) = 44*(4+4)
353 (4) = (gamma(4)!-gamma(4))/sqrt(4)-4
354 (4) = (4!-.4)*gamma(4)/.4
355 (4) = (4!*gamma(4)-sqrt(4))/.4
356 (0) = (4!/4)!/sqrt(4)-4
357 (4) = (gamma(4)!-4!/4)/sqrt(4)
358 (0) = ((4!/4)!-4)/sqrt(4)
359 (0) = ((4!/4)!-sqrt(4))/sqrt(4)
360 (0) = 4*4*4!-4!
361 (0) = (4!-sqrt(4)/.4)^sqrt(4)
362 (0) = ((4!/4)!+4)/sqrt(4)
363 (4) = root(.4,4/.4~)+gamma(gamma(4))
364 (0) = (4!/4)!/sqrt(4)+4
365 (4) = (4!*gamma(4)+sqrt(4))/.4
366 (4) = (4!+.4)*gamma(4)/.4
367 (4) = (gamma(4)!+gamma(4))/sqrt(4)+4
368 (0) = 4*(4*4!-4)
369 (4) = (gamma(gamma(4))+44)/.4~
370 (4) = (4!*gamma(4)+4)/.4
371 (4) = (gamma(4)!-sqrt(4)+4!)/sqrt(4)
372 (0) = ((4!/4)!+4!)/sqrt(4)
373 (4) = (gamma(4)!+4!+sqrt(4))/sqrt(4)
374 (4) = 4^4-sqrt(4)+gamma(gamma(4))
375 (0) = 4!/.4/.4/.4
376 (0) = 4*(4*4!-sqrt(4))
377 (4) = gamma(sqrt(4))+gamma(gamma(4))+4^4
378 (2) = (4^4-4)/sqrt(.4~)
379 (5) = gamma(4)/.4/4%+4
380 (0) = 4*4*4!-4
381 (2) = (4^4-sqrt(4))/sqrt(.4~)
382 (0) = 4*4*4!-sqrt(4)
383 (4) = 4*4*4!-gamma(sqrt(4))
384 (0) = 4!*(4!-4-4)
385 (4) = 4*4*4!+gamma(sqrt(4))
386 (0) = 4*4*4!+sqrt(4)
387 (2) = (sqrt(4)+4^4)/sqrt(.4~)
388 (0) = 4*4*4!+4
389 (4) = (gamma(4)^gamma(4)+4!)/gamma(gamma(4))
390 (2) = (4^4+4)/sqrt(.4~)
391 (4) = (gamma(gamma(4))+.4~)/.4~+gamma(gamma(4))
392 (0) = 4*(4*4!+sqrt(4))
393 (4) = (gamma(4)+4^4)/sqrt(.4~)
394 (4) = sqrt((4-4!)^4)-gamma(4)
395 (5) = (4*4-sqrt(4%))/4%
396 (0) = sqrt((4-4!)^4)-4
397 (6) = square(4)/4%-sqrt(4/.4~)
398 (0) = sqrt((4-4!)^4)-sqrt(4)
399 (4) = (gamma(4)!/.4~-4!)/4
400 (0) = 4*(4*4!+4)
401 (4) = gamma(4)!/.4~/4-4
402 (0) = sqrt((4-4!)^4)+sqrt(4)
403 (4) = gamma(4)!/.4~/4-sqrt(4)
404 (0) = sqrt((4-4!)^4)+4
405 (2) = (4!/4)!/4/.4~
406 (4) = (gamma(4)!/.4~+4)/4
407 (4) = gamma(4)!/.4~/4+sqrt(4)
408 (0) = 4*4*4!+4!
409 (4) = gamma(4)!/.4~/4+4
410 (4) = (gamma(gamma(4))+44)/.4
411 (4) = (gamma(4)!/.4~+4!)/4
412 (4) = .4*gamma(4)!+gamma(gamma(4))+4
413 (6) = (gamma(sqrt(4))/.4%+square(4!))/sqrt(4)
414 (4) = (gamma(4)!/4+4)/.4~
415 (4) = gamma(4)!-(gamma(gamma(4))+sqrt(4))/.4
416 (0) = 4*4*(sqrt(4)+4!)
417 (4) = (gamma(gamma(4))-gamma(4)+gamma(4)!)/sqrt(4)
418 (4) = gamma(4)!-gamma(gamma(4))/.4-sqrt(4)
419 (4) = gamma(4)!-(gamma(gamma(4))+.4)/.4
420 (0) = 444-4!
421 (4) = (gamma(gamma(4))+.4)/.4+gamma(gamma(4))
422 (4) = gamma(4)!-gamma(gamma(4))/.4+sqrt(4)
423 (4) = (.4*gamma(4)!-gamma(4))/sqrt(.4~)
424 (0) = sqrt((4-4!)^4)+4!
425 (4) = gamma(4)!-(gamma(gamma(4))-sqrt(4))/.4
426 (4) = gamma(4)!/4/.4-4!
427 (6) = square(4!)-(gamma(4)-4%)/4%
428 (4) = (4-.4)*gamma(gamma(4))-4
429 (4) = gamma(4)!/.4~/4+4!
430 (4) = (4-.4)*gamma(gamma(4))-sqrt(4)
431 (4) = (4-.4)*gamma(gamma(4))-gamma(sqrt(4))
432 (0) = 4!*(sqrt(4)+4*4)
433 (4) = (4-.4)*gamma(gamma(4))+gamma(sqrt(4))
434 (4) = (4-.4)*gamma(gamma(4))+sqrt(4)
435 (4) = (gamma(4)!-4!)/.4/4
436 (4) = 4*gamma(gamma(4))-44
437 (6) = square(gamma(4)/.4+gamma(4))-4
438 (4) = 444-gamma(4)
439 (4) = gamma(gamma(4))-gamma(sqrt(4))+.4~*gamma(4)!
440 (0) = 444-4
441 (2) = (4!-sqrt(4/.4~))^sqrt(4)
442 (0) = 444-sqrt(4)
443 (4) = 444-gamma(sqrt(4))
444 (0) = sqrt(444^sqrt(4))
445 (4) = gamma(sqrt(4))+444
446 (0) = sqrt(4)+444
447 (4) = (gamma(gamma(4))/.4-sqrt(4))/sqrt(.4~)
448 (0) = 444+4
449 (4) = (gamma(4)!/.4-4)/4
450 (0) = (4!/4)!/.4/4
451 (4) = (gamma(4)!/.4+4)/4
452 (4) = 4*gamma(gamma(4))-4!-4
453 (4) = (gamma(gamma(4))/.4+sqrt(4))/sqrt(.4~)
454 (4) = gamma(4)!/4/.4+4
455 (4) = (gamma(4)!/4+sqrt(4))/.4
456 (0) = 4!*(4!-4)-4!
457 (4) = 4*gamma(gamma(4))-4!+gamma(sqrt(4))
458 (4) = gamma(4)!-gamma(4)-4^4
459 (4) = (gamma(4)!/4+4!)/.4~
460 (0) = (4!-sqrt(4))^sqrt(4)-4!
461 (6) = .4*sqrt(4)*square(4!)+sqrt(4%)
462 (4) = gamma(4)!-sqrt(4)-4^4
463 (4) = gamma(4)!-gamma(sqrt(4))-4^4
464 (0) = (4!/4)!-4^4
465 (4) = (gamma(4)!+4!)/4/.4
466 (4) = gamma(4)!+sqrt(4)-4^4
467 (6) = (square(square(gamma(4)))+square(4!)-4)/4
468 (0) = 4!+444
469 (4) = 4*gamma(gamma(4))-sqrt(gamma(sqrt(4))+gamma(gamma(4)))
470 (4) = 4*gamma(gamma(4))-4/.4
471 (4) = 4*gamma(gamma(4))-4/.4~
472 (0) = (4!-4)*(4!-.4)
473 (4) = 4*gamma(gamma(4))-gamma(sqrt(4))-gamma(4)
474 (4) = gamma(4)!/4/.4+4!
475 (4) = 4*gamma(gamma(4))-sqrt(4)/.4
476 (0) = 4!*(4!-4)-4
477 (4) = gamma(4)!-root(.4,4/.4~)
478 (0) = 4!*(4!-4)-sqrt(4)
479 (4) = 4*gamma(gamma(4))-4/4
480 (0) = 4*(4/4+4)!
481 (4) = 4*gamma(gamma(4))+4/4
482 (0) = 4!*(4!-4)+sqrt(4)
483 (4) = 4*gamma(gamma(4))+sqrt(4/.4~)
484 (0) = 44^sqrt(4)/4
485 (4) = 4*gamma(gamma(4))+sqrt(4)/.4
486 (0) = (4!-sqrt(4))^sqrt(4)+sqrt(4)
487 (4) = 4*gamma(gamma(4))+gamma(sqrt(4))+gamma(4)
488 (0) = (4!-4)*(4!+.4)
489 (4) = 4*gamma(gamma(4))+4/.4~
490 (4) = 4*gamma(gamma(4))+4/.4
491 (4) = sqrt(gamma(sqrt(4))+gamma(gamma(4)))+4*gamma(gamma(4))
492 (4) = 4*(gamma(gamma(4))+4)-4
493 (5) = (sqrt(4)-.4%)/.4%-gamma(4)
494 (4) = 4*(gamma(gamma(4))+4)-sqrt(4)
495 (4) = 4*gamma(gamma(4))+gamma(4)/.4
496 (0) = 4*((sqrt(4)/.4)!+4)
497 (4) = 4*(gamma(gamma(4))+4)+gamma(sqrt(4))
498 (4) = 4*(gamma(gamma(4))+4)+sqrt(4)
499 (5) = sqrt(4)/.4%-4/4
500 (0) = 4*sqrt(sqrt(sqrt((sqrt(4)/.4)^4!)))
501 (5) = sqrt(4)/.4%+4/4
502 (4) = 4*(gamma(gamma(4))+4)+gamma(4)
503 (4) = 4!-gamma(sqrt(4))+4*gamma(gamma(4))
504 (0) = sqrt(4)*(4^4-4)
505 (4) = (sqrt(4)/.4)^4-gamma(gamma(4))
506 (4) = 4^4*sqrt(4)-gamma(4)
507 (5) = (sqrt(4)+.4%)/.4%+gamma(4)
508 (0) = 4^4*sqrt(4)-4
509 (5) = sqrt(4)/.4%+4/.4~
510 (0) = 4^4*sqrt(4)-sqrt(4)
511 (4) = 4^4*sqrt(4)-gamma(sqrt(4))
512 (0) = 4^4+4^4
513 (4) = 4^4*sqrt(4)+gamma(sqrt(4))
514 (0) = 4^4*sqrt(4)+sqrt(4)
515 (4) = (gamma(sqrt(4))+gamma(4)!)/(gamma(sqrt(4))+.4)
516 (0) = 4^4*sqrt(4)+4
517 (6) = square(4!)-(4!-.4)/.4
518 (4) = .4*gamma(4)^4-.4
519 (6) = (gamma(4)/.4%+square(4!))/4
520 (0) = sqrt(4)*(4^4+4)
521 (6) = root(.4~,square(4))+4/.4~
522 (2) = (4^4-4!)/.4~
523 (4) = (4!-gamma(sqrt(4)))^sqrt(4)-gamma(4)
524 (0) = 4!*(4!-sqrt(4))-4
525 (4) = gamma(4+4)/4!/.4
526 (0) = 4!*(4!-sqrt(4))-sqrt(4)
527 (4) = 4!*(4!-sqrt(4))-gamma(sqrt(4))
528 (0) = 44*4!/sqrt(4)
529 (0) = (4!-4/4)^sqrt(4)
530 (0) = 4!*(4!-sqrt(4))+sqrt(4)
531 (4) = (sqrt(4)*gamma(gamma(4))-4)/.4~
532 (0) = 4!*4!-44
533 (4) = (4!-gamma(sqrt(4)))^sqrt(4)+4
534 (4) = 4*gamma(gamma(4))+4!/.4~
535 (4) = (sqrt(gamma(4)^gamma(4))-sqrt(4))/.4
536 (0) = 4^4*sqrt(4)+4!
537 (4) = (gamma(4)!-4)/sqrt(4*.4~)
538 (4) = sqrt(gamma(4)^gamma(4))/.4-sqrt(4)
539 (4) = (sqrt(gamma(4)^gamma(4))-.4)/.4
540 (0) = sqrt(sqrt(sqrt((4!/4)^4!)))/.4
541 (4) = (sqrt(gamma(4)^gamma(4))+.4)/.4
542 (4) = sqrt(gamma(4)^gamma(4))/.4+sqrt(4)
543 (4) = (gamma(4)!+4)/sqrt(4*.4~)
544 (2) = 4!*(4!-sqrt(4*.4~))
545 (4) = (sqrt(gamma(4)^gamma(4))+sqrt(4))/.4
546 (4) = 4!*4!-gamma(4)-4!
547 (6) = square(4!)-sqrt(4)/.4-4!
548 (0) = 4!*4!-4-4!
549 (4) = (sqrt(4)*gamma(gamma(4))+4)/.4~
550 (0) = 4!*4!-4!-sqrt(4)
551 (4) = 4!*4!-gamma(sqrt(4))-4!
552 (0) = 4!*(4!-4/4)
553 (4) = 4!*4!-4!+gamma(sqrt(4))
554 (0) = 4!*4!+sqrt(4)-4!
555 (4) = (sqrt(gamma(4)^gamma(4))+gamma(4))/.4
556 (0) = 4!*4!+4-4!
557 (5) = (4!-.4)^sqrt(4)+4%
558 (2) = 4!*(4!-sqrt(.4~))-sqrt(4)
559 (4) = 4!*(4!-sqrt(.4~))-gamma(sqrt(4))
560 (0) = 4!*4!-4*4
561 (4) = 4!*4!-gamma(4)/.4
562 (2) = 4!*(4!-sqrt(.4~))+sqrt(4)
563 (6) = square(4!)-4-4/.4~
564 (0) = 4!*(4!-sqrt(4)/4)
565 (4) = 4!*4!-sqrt(gamma(sqrt(4))+gamma(gamma(4)))
566 (0) = 4!*4!-4/.4
567 (2) = (4^4-4)/.4~
568 (0) = 4!*4!-4-4
569 (4) = 4!*4!-gamma(4)-gamma(sqrt(4))
570 (0) = 4!*4!-4!/4
571 (0) = 4!*4!-sqrt(4)/.4
572 (0) = 4!^(4-sqrt(4))-4
573 (2) = 4!*4!-sqrt(4/.4~)
574 (0) = 4!*4!+sqrt(4)-4
575 (0) = 4!*4!-4/4
576 (0) = 4!*(4.4-.4)!
577 (0) = 4!*4!+4/4
578 (0) = 4!*4!+4-sqrt(4)
579 (2) = sqrt(4/.4~)+4!*4!
580 (0) = (4^4-4!)/.4
581 (0) = 4!*4!+sqrt(4)/.4
582 (0) = 4!*4!+4!/4
583 (4) = 4!*4!+gamma(sqrt(4))+gamma(4)
584 (0) = 4!*4!+4+4
585 (2) = (4^4+4)/.4~
586 (0) = 4!*4!+4/.4
587 (4) = sqrt(gamma(sqrt(4))+gamma(gamma(4)))+4!*4!
588 (0) = 4!*(sqrt(4)/4+4!)
589 (4) = gamma(4)!-gamma(gamma(4))-sqrt(gamma(sqrt(4))+gamma(gamma(4)))
590 (2) = 4!*(sqrt(.4~)+4!)-sqrt(4)
591 (4) = 4!*4!+gamma(4)/.4
592 (0) = 4!*4!+4*4
593 (4) = 4!*(sqrt(.4~)+4!)+gamma(sqrt(4))
594 (2) = 4!*(sqrt(.4~)+4!)+sqrt(4)
595 (4) = (sqrt(4)*gamma(gamma(4))-sqrt(4))/.4
596 (0) = 4!*4!+4!-4
597 (4) = gamma(4)!-gamma(gamma(4))-sqrt(4/.4~)
598 (0) = 4!*4!+4!-sqrt(4)
599 (4) = (sqrt(4)*gamma(gamma(4))-.4)/.4
600 (0) = 4*4!/.4/.4
601 (0) = (sqrt(4)/.4)^4-4!
602 (0) = 4!*4!+sqrt(4)+4!
603 (4) = (gamma(gamma(4))/.4~-sqrt(4))/.4~
604 (0) = 4!*4!+4!+4
605 (4) = (sqrt(4)*gamma(gamma(4))+sqrt(4))/.4
606 (4) = 4!*4!+4!+gamma(4)
607 (4) = (.4~+.4)*gamma(4)!-gamma(sqrt(4))
608 (2) = (.4~+.4)*(4!/4)!
609 (4) = gamma(4)!-gamma(gamma(4))+4/.4~
610 (4) = gamma(4)!-44/.4
611 (4) = root(sqrt(.4~),gamma(sqrt(4))+gamma(gamma(4)))-gamma(4)!
612 (2) = 4!/sqrt(.4~)+4!*4!
613 (6) = square(gamma(4))+square(4!)+4/4
614 (4) = (.4~+.4)*gamma(4)!+gamma(4)
615 (4) = (gamma(gamma(4))/.4~-4!)/.4
616 (0) = 4^4/.4-4!
617 (6) = (square(4)+.4)/.4+square(4!)
618 (4) = gamma(4)!-gamma(4)-4*4!
619 (4) = (sqrt(4)/.4)^4-gamma(4)
620 (0) = 4!*4!+44
621 (0) = (sqrt(4)/.4)^4-4
622 (0) = 4!*(sqrt(4)+4!)-sqrt(4)
623 (0) = (sqrt(4)/.4)^4-sqrt(4)
624 (0) = (4!/4)!-4*4!
625 (0) = (4/4+4)^4
626 (0) = 4!*(sqrt(4)+4!)+sqrt(4)
627 (0) = (sqrt(4)/.4)^4+sqrt(4)
628 (0) = 4!*(sqrt(4)+4!)+4
629 (0) = (sqrt(4)/.4)^4+4
630 (0) = (4^4-4)/.4
631 (4) = (sqrt(4)/.4)^4+gamma(4)
632 (4) = gamma(4)!-44*sqrt(4)
633 (6) = square(square(sqrt(4)/.4))+4+4
634 (4) = 4^4/.4-gamma(4)
635 (0) = (4^4-sqrt(4))/.4
636 (0) = 4^4/.4-4
637 (6) = (4!+.4)/.4+square(4!)
638 (0) = 4^4/.4-sqrt(4)
639 (0) = (4^4-.4)/.4
640 (0) = sqrt(4*4)^4/.4
641 (4) = gamma(sqrt(4))+4^4/.4
642 (0) = 4^4/.4+sqrt(4)
643 (6) = (square(square(4))-.4)/.4+4
644 (0) = 4^4/.4+4
645 (0) = (sqrt(4)+4^4)/.4
646 (0) = (sqrt(4)+4!)!/4!!-4
647 (4) = (gamma(4)^4-sqrt(4))/sqrt(4)
648 (0) = (4!/4)^4/sqrt(4)
649 (0) = (sqrt(4)/.4)^4+4!
650 (0) = (4^4+4)/.4
651 (4) = (gamma(4)^4+gamma(4))/sqrt(4)
652 (0) = (sqrt(4)+4!)^sqrt(4)-4!
653 (6) = square(4!)-4+square(4/.4~)
654 (0) = (sqrt(4)+4!)!/4!!+4
655 (4) = (gamma(4)+4^4)/.4
656 (0) = (4!/4)!-sqrt(sqrt(sqrt(4)^4!))
657 (4) = (.4*gamma(4)!+4)/.4~
658 (4) = gamma(4)!-4!/.4-sqrt(4)
659 (4) = gamma(4)!-(4!+.4)/.4
660 (0) = (4!/4)!-4!/.4
661 (4) = gamma(4)!-(4!-.4)/.4
662 (4) = gamma(4)!-4!/.4~-4
663 (4) = gamma(4)!-(gamma(gamma(4))-gamma(4))/sqrt(4)
664 (0) = 4^4/.4+4!
665 (4) = (gamma(gamma(4))/.4~-4)/.4
666 (2) = 444/sqrt(.4~)
667 (4) = gamma(4)!-(4!-.4~)/.4~
668 (0) = 4!*(4!+4)-4
669 (4) = gamma(gamma(4))/.4/.4~-gamma(4)
670 (0) = 4!*(4!+4)-sqrt(4)
671 (4) = gamma(gamma(4))/.4/.4~-4
672 (0) = .4/4!*(4+4)!
673 (4) = 4!*(4!+4)+gamma(sqrt(4))
674 (0) = 4!*(4!+4)+sqrt(4)
675 (2) = (sqrt(4)/.4)!/.4/.4~
676 (0) = (4!/4)!-44
677 (4) = gamma(sqrt(4))+gamma(4)!-44
678 (0) = (sqrt(4)+4!)^sqrt(4)+sqrt(4)
679 (4) = gamma(gamma(4))/.4/.4~+4
680 (0) = (sqrt(4)+4!)^sqrt(4)+4
681 (4) = gamma(4)!-gamma(4)/.4-4!
682 (4) = gamma(4)-44+gamma(4)!
683 (4) = (sqrt(sqrt(4)^4!)+sqrt(4))/gamma(4)
684 (2) = 4!*(sqrt(4)/.4~+4!)
685 (4) = (gamma(gamma(4))/.4~+4)/.4
686 (4) = gamma(4)!-4!-4/.4
687 (4) = gamma(4)!-4!-4/.4~
688 (2) = 4!*(sqrt(.4~)+4!+4)
689 (4) = gamma(4)!-(gamma(gamma(4))+4)/4
690 (4) = gamma(4)!-4!/(.4+.4)
691 (4) = gamma(4)!-sqrt(4)/.4-4!
692 (0) = (4!/4)!-4!-4
693 (4) = gamma(4)!-4!/(.4~+.4~)
694 (0) = (4!/4)!-4!-sqrt(4)
695 (4) = gamma(4)!-4/.4/.4
696 (0) = (4/.4-4)!-4!
697 (4) = gamma(4)!-4!+4/4
698 (0) = (4!/4)!-4!+sqrt(4)
699 (4) = gamma(gamma(4))/.4/.4~+4!
700 (0) = (4^4+4!)/.4
701 (4) = gamma(4)!-gamma(4)/.4-4
702 (4) = gamma(4)!-4*4-sqrt(4)
703 (4) = gamma(4)!-gamma(sqrt(4))-4*4
704 (0) = 4*4*44
705 (2) = sqrt(sqrt(sqrt(4/.4~)^4!))-4!
706 (4) = gamma(4)!-4/.4-4
707 (4) = gamma(4)!-4-4/.4~
708 (0) = (4!/4)!-4!/sqrt(4)
709 (4) = gamma(4)!-44/4
710 (0) = (4!/4)!-4/.4
711 (2) = (4!/4)!-4/.4~
712 (0) = (4!/4)!-4-4
713 (4) = gamma(4)!-(4!+4)/4
714 (0) = (4!/4)!-4!/4
715 (0) = (4!/4)!-sqrt(4)/.4
716 (0) = (4/.4-4)!-4
717 (2) = (4!/4)!-sqrt(4/.4~)
718 (0) = (4/.4-4)!-sqrt(4)
719 (0) = (4!/4)!-4/4
720 (0) = (4*.4+4.4)!
721 (0) = (4!/4)!+4/4
722 (0) = (4/.4-4)!+sqrt(4)
723 (2) = sqrt(4/.4~)+(4!/4)!
724 (0) = (4/.4-4)!+4
725 (0) = (4!/4)!+sqrt(4)/.4
726 (0) = (4!/4)!+4!/4
727 (2) = sqrt(sqrt(sqrt(4/.4~)^4!))-sqrt(4)
728 (0) = (4!/4)!+4+4
729 (0) = sqrt(sqrt((4-4/4)^4!))
730 (0) = (4!/4)!+4/.4
731 (2) = sqrt(sqrt(sqrt(4/.4~)^4!))+sqrt(4)
732 (0) = 4!/sqrt(4)+(4!/4)!
733 (2) = sqrt(sqrt(sqrt(4/.4~)^4!))+4
734 (4) = gamma(4)!+4/.4+4
735 (4) = 4!/4/.4+gamma(4)!
736 (0) = (4!/4)!+4*4
737 (4) = gamma(4)!+4*4+gamma(sqrt(4))
738 (4) = gamma(4)!+sqrt(4)+4*4
739 (4) = gamma(4)/.4+gamma(4)!+4
740 (0) = (4!/4)!+4!-4
741 (4) = gamma(4)!+gamma(4)+gamma(4)/.4
742 (0) = (4!/4)!+4!-sqrt(4)
743 (4) = gamma(4)!+4!-4/4
744 (0) = (4/.4-4)!+4!
745 (4) = gamma(4)!+4/.4/.4
746 (0) = (4!/4)!+sqrt(4)+4!
747 (4) = 4!/(.4~+.4~)+gamma(4)!
748 (0) = (4!/4)!+4!+4
749 (4) = (gamma(gamma(4))/.4-.4)/.4
750 (0) = (sqrt(4)/.4)!/.4/.4
751 (4) = (gamma(gamma(4))+4)/4+gamma(4)!
752 (3) = (4!/4)!+root(.4,4)
753 (2) = sqrt(sqrt(sqrt(4/.4~)^4!))+4!
754 (4) = gamma(gamma(4))/.4/.4+4
755 (4) = (gamma(gamma(4))/.4+sqrt(4))/.4
756 (2) = 4!/sqrt(.4~)+(4!/4)!
757 (4) = sqrt(gamma(4))^4+gamma(4)!+gamma(sqrt(4))
758 (4) = gamma(4)!-gamma(4)+44
759 (4) = gamma(4)!+4!+gamma(4)/.4
760 (0) = sqrt((4!+4)^4)-4!
761 (6) = (square(4)+.4)/.4+gamma(4)!
762 (4) = gamma(4)!-sqrt(4)+44
763 (4) = gamma(4)!-gamma(sqrt(4))+44
764 (0) = (4!/4)!+44
765 (4) = gamma(sqrt(4))+gamma(4)!+44
766 (3) = 4!*root(.4,4)-sqrt(4)
767 (4) = 4!*root(.4,4)-gamma(sqrt(4))
768 (0) = 4*4!*(4+4)
769 (4) = 4!*root(.4,4)+gamma(sqrt(4))
770 (3) = 4!*root(.4,4)+sqrt(4)
771 (5) = (sqrt(4)+4%)/4%+gamma(4)!
772 (3) = 4!*root(.4,4)+4
773 (4) = (4!-.4~)/.4~+gamma(4)!
774 (2) = (4!/4)!+4!/.4~
775 (4) = (gamma(gamma(4))+4)/.4/.4
776 (4) = gamma(4)!+4!/.4-4
777 (4) = (gamma(gamma(4))-gamma(4))/sqrt(4)+gamma(4)!
778 (4) = sqrt((4!+4)^4)-gamma(4)
779 (4) = (4!-.4)/.4+gamma(4)!
780 (0) = sqrt((4!+4)^4)-4
781 (4) = gamma(4)!+4!/.4+gamma(sqrt(4))
782 (0) = sqrt((4!+4)^4)-sqrt(4)
783 (4) = (4!+4)/.4~+gamma(4)!
784 (0) = (4!+4)*(4!+4)
785 (4) = (.4~*gamma(4)!-gamma(4))/.4
786 (0) = sqrt((4!+4)^4)+sqrt(4)
787 (6) = sqrt(4/.4~)+square(4!+4)
788 (0) = sqrt((4!+4)^4)+4
789 (6) = square(4!+4)+sqrt(4)/.4
790 (4) = (4!+4)/.4+gamma(4)!
791 (4) = sqrt(gamma(sqrt(4))+gamma(4+4))+gamma(4)!
792 (2) = 4!*(4/.4~+4!)
793 (6) = square(4!+4)+4/.4~
794 (4) = .4~*gamma(4)!/.4-gamma(4)
795 (4) = (gamma(4)+4!)/.4+gamma(4)!
796 (4) = .4~*gamma(4)!/.4-4
797 (6) = square(4/.4~)+gamma(4)!-4
798 (4) = .4~*gamma(4)!/.4-sqrt(4)
799 (4) = (.4~*gamma(4)!-.4)/.4
800 (0) = sqrt(4*(4!-4)^4)
801 (4) = sqrt(4/.4~)^4+gamma(4)!
802 (4) = .4~*gamma(4)!/.4+sqrt(4)
803 (6) = (square(square(4)/.4)+gamma(4))/sqrt(4)
804 (4) = .4~*gamma(4)!/.4+4
805 (4) = (.4~*gamma(4)!+sqrt(4))/.4
806 (4) = gamma(4)!/(.4~+.4~)-4
807 (4) = (gamma(4)!/.4~-gamma(4))/sqrt(4)
808 (0) = sqrt((4!+4)^4)+4!
809 (4) = (gamma(4)!/sqrt(4)-.4~)/.4~
810 (2) = (4!/4)!/(.4~+.4~)
811 (4) = (gamma(4)!/.4~+sqrt(4))/sqrt(4)
812 (4) = gamma(4)!-4+4*4!
813 (4) = (gamma(4)!/.4~+gamma(4))/sqrt(4)
814 (4) = gamma(4)!/(.4~+.4~)+4
815 (4) = (.4~*gamma(4)!+gamma(4))/.4
816 (0) = 4!*(4/.4+4!)
817 (4) = gamma(sqrt(4))+gamma(4)!+4*4!
818 (4) = gamma(4)!+sqrt(4)+4*4!
819 (4) = gamma(4)!+44/.4~
820 (4) = gamma(4)!+4*4!+4
821 (5) = (4%+4)/4%+gamma(4)!
822 (4) = gamma(4)!+gamma(4)+4*4!
823 (6) = square(square(4))+square(4!)-4/.4~
824 (4) = .4~*gamma(4)!/.4+4!
825 (4) = gamma(4)!-gamma(4)/.4+gamma(gamma(4))
826 (4) = (gamma(sqrt(4))+gamma(4))*(gamma(gamma(4))-sqrt(4))
827 (6) = square(square(4))+square(4!)-sqrt(4)/.4
828 (2) = (4!*4!-4!)/sqrt(.4~)
829 (4) = gamma(gamma(4))-sqrt(gamma(sqrt(4))+gamma(gamma(4)))+gamma(4)!
830 (4) = gamma(4)!+44/.4
831 (4) = gamma(gamma(4))+gamma(4)!-4/.4~
832 (0) = 4!*4!+4^4
833 (4) = gamma(gamma(4))-gamma(sqrt(4))-gamma(4)+gamma(4)!
834 (4) = gamma(4+4)/gamma(4)-gamma(4)
835 (4) = gamma(4)!-sqrt(4)/.4+gamma(gamma(4))
836 (4) = gamma(4+4)/gamma(4)-4
837 (4) = (gamma(4)!+4!)/(.4~+.4~)
838 (4) = gamma(4+4)/gamma(4)-sqrt(4)
839 (4) = (gamma(4+4)-gamma(4))/gamma(4)
840 (0) = (4+4)!/(4!+4!)
841 (0) = (sqrt(4)/.4+4!)^sqrt(4)
842 (4) = gamma(4+4)/gamma(4)+sqrt(4)
843 (4) = sqrt(4/.4~)+gamma(4)!+gamma(gamma(4))
844 (4) = gamma(4+4)/gamma(4)+4
845 (4) = sqrt(4)/.4+gamma(4)!+gamma(gamma(4))
846 (4) = (gamma(gamma(4))+4^4)/.4~
847 (4) = gamma(sqrt(4))+gamma(gamma(4))+gamma(4)!+gamma(4)
848 (2) = (4!-.4~)*4!/sqrt(.4~)
849 (4) = gamma(gamma(4))+gamma(4)!+4/.4~
850 (4) = gamma(gamma(4))+4/.4+gamma(4)!
851 (4) = sqrt(gamma(sqrt(4))+gamma(gamma(4)))+gamma(4)!+gamma(gamma(4))
852 (4) = gamma(4)*(4!*gamma(4)-sqrt(4))
853 (6) = (square(4!)-gamma(4))/sqrt(.4~)-sqrt(4)
854 (4) = (gamma(gamma(4))+sqrt(4))*(gamma(sqrt(4))+gamma(4))
855 (4) = 4!/.4/.4~+gamma(4)!
856 (4) = gamma(gamma(4))+4*4+gamma(4)!
857 (6) = (square(4!)-sqrt(4))/sqrt(.4~)-4
858 (2) = (4!*4!-4)/sqrt(.4~)
859 (6) = 4!*square(gamma(4))-sqrt(4)/.4
860 (2) = sqrt(4!^4/.4~)-4
861 (2) = (4!*4!-sqrt(4))/sqrt(.4~)
862 (2) = sqrt(4!^4/.4~)-sqrt(4)
863 (4) = sqrt(4!^4/.4~)-gamma(sqrt(4))
864 (0) = 4!*(4!/.4-4!)
865 (4) = sqrt(4!^4/.4~)+gamma(sqrt(4))
866 (2) = sqrt(4!^4/.4~)+sqrt(4)
867 (2) = (4!*4!+sqrt(4))/sqrt(.4~)
868 (2) = sqrt(4!^4/.4~)+4
869 (5) = (gamma(4)-4%)/4%+gamma(4)!
870 (2) = (4!*4!+4)/sqrt(.4~)
871 (5) = (gamma(4)+4%)/4%+gamma(4)!
872 (4) = gamma(gamma(4))+gamma(4)!+root(.4,4)
873 (4) = (4!*4!+gamma(4))/sqrt(.4~)
874 (5) = gamma(4)/4%+gamma(4)!+4
875 (5) = (4-sqrt(4)/4)/.4%
876 (4) = gamma(4)!/(.4+.4)-4!
877 (6) = (gamma(gamma(4))+.4)/.4+square(4!)
878 (5) = 4/.4%-sqrt(4)-gamma(gamma(4))
879 (5) = (4-.4%)/.4%-gamma(gamma(4))
880 (0) = 44*(4!-4)
881 (5) = 4/.4%-gamma(gamma(4))+gamma(sqrt(4))
882 (4) = gamma(4)!/4.4~+gamma(4)!
883 (6) = (square(gamma(4))-4%)/4%-square(4)
884 (4) = gamma(gamma(4))+gamma(4)!+44
885 (4) = (gamma(4)!/sqrt(4)-gamma(4))/.4
886 (5) = 4/.4%-gamma(gamma(4))+gamma(4)
887 (6) = 4!*square(gamma(4))-gamma(sqrt(4))+4!
888 (0) = 444*sqrt(4)
889 (6) = (square(gamma(4))-.44)/4%
890 (4) = (gamma(4)!/sqrt(4)-4)/.4
891 (4) = (gamma(4)!-4)/.4~-gamma(4)!
892 (6) = square(gamma(4))/4%-4-4
893 (6) = (square(gamma(4))-4%)/4%-gamma(4)
894 (4) = gamma(4)!/(.4+.4)-gamma(4)
895 (4) = (gamma(4)!-4)/(.4+.4)
896 (2) = 4!*4!*(sqrt(4)-.4~)
897 (4) = (gamma(4)!/.4-gamma(4))/sqrt(4)
898 (4) = (gamma(4)!/.4-4)/sqrt(4)
899 (4) = (gamma(4)!/sqrt(4)-.4)/.4
900 (0) = (4!/4)!/(.4+.4)
901 (4) = (gamma(4)!+4)/4+gamma(4)!
902 (4) = (gamma(4)!/.4+4)/sqrt(4)
903 (4) = (gamma(4)!/.4+gamma(4))/sqrt(4)
904 (4) = gamma(4)!/(.4+.4)+4
905 (4) = (gamma(4)!+4)/(.4+.4)
906 (4) = gamma(4)!/(.4+.4)+gamma(4)
907 (6) = (square(gamma(4))+4%)/4%+gamma(4)
908 (5) = root(sqrt(4%),4)-gamma(gamma(4))+4
909 (4) = (gamma(4)!+4)/.4~-gamma(4)!
910 (4) = (gamma(4)!/sqrt(4)+4)/.4
911 (6) = (square(gamma(4))+.4)/4%+gamma(sqrt(4))
912 (2) = 4!*(4!/sqrt(.4~)+sqrt(4))
913 (6) = square(square(sqrt(4)/.4))+.4*gamma(4)!
914 (6) = (square(gamma(4))+.4)/4%+4
915 (4) = (gamma(4)!/sqrt(4)+gamma(4))/.4
916 (6) = square(4)-(.4-4)/.4%
917 (6) = (square(gamma(4))+4%)/4%+square(4)
918 (4) = (.4*gamma(4)!+gamma(gamma(4)))/.4~
919 (6) = 4/.4%-square(4/.4~)
920 (4) = gamma(4)!/(4-.4)+gamma(4)!
921 (6) = gamma(4)!-4!+square(gamma(4)/.4)
922 (6) = 4*.4*square(4!)+.4
923 (6) = (square(gamma(4))-4%)/4%+4!
924 (4) = gamma(4)!/(.4+.4)+4!
925 (5) = (4-sqrt(4%/.4~))/.4%
926 (6) = (square(gamma(4))+.4)/4%+square(4)
927 (6) = sqrt(4)*square(4!)-square(gamma(4)/.4)
928 (0) = 4*(4^4-4!)
929 (6) = (square(gamma(4))+gamma(sqrt(4)))/4%+4
930 (4) = (gamma(4)!+4!)/(.4+.4)
931 (6) = gamma(gamma(4))/.4/.4~+square(square(4))
932 (4) = sqrt(gamma(4)^gamma(4))+gamma(4)!-4
933 (6) = (gamma(4)!-gamma(4))/sqrt(4)+square(4!)
934 (4) = sqrt(gamma(4)^gamma(4))+gamma(4)!-sqrt(4)
935 (4) = gamma(4)!-gamma(sqrt(4))+sqrt(gamma(4)^gamma(4))
936 (2) = (sqrt(4)+4!)*4!/sqrt(.4~)
937 (4) = sqrt(gamma(4)^gamma(4))+gamma(4)!+gamma(sqrt(4))
938 (4) = sqrt(gamma(4)^gamma(4))+gamma(4)!+sqrt(4)
939 (6) = (square(square(4))+gamma(gamma(4))-.4)/.4
940 (4) = (gamma(gamma(4))+4^4)/.4
941 (6) = square(gamma(4)/.4)+gamma(4)!-4
942 (4) = sqrt(gamma(4)^gamma(4))+gamma(4)!+gamma(4)
943 (6) = root(sqrt(4%),4)-square(4/.4~)
944 (4) = 4*(sqrt(4)*gamma(gamma(4))-4)
945 (4) = (gamma(4)/.4)^sqrt(4)+gamma(4)!
946 (5) = 4/.4%-4!/.4~
947 (6) = square(gamma(4)/.4)+sqrt(4)+gamma(4)!
948 (4) = sqrt(4)*(4*gamma(gamma(4))-gamma(4))
949 (6) = square(gamma(4)/.4)+gamma(4)!+4
950 (5) = (44-gamma(4))/4%
951 (4) = (gamma(4)!-gamma(4))/sqrt(.4~)-gamma(gamma(4))
952 (4) = gamma(4)!-4!+4^4
953 (6) = gamma(4)!-4!+gamma(sqrt(4))+square(square(4))
954 (4) = (4+4)*gamma(gamma(4))-gamma(4)
955 (6) = (4!*square(4)-sqrt(4))/.4
956 (4) = (4+4)*gamma(gamma(4))-4
957 (4) = (gamma(4)!-sqrt(4))/sqrt(.4~)-gamma(gamma(4))
958 (4) = (4+4)*gamma(gamma(4))-sqrt(4)
959 (4) = (4+4)*gamma(gamma(4))-gamma(sqrt(4))
960 (0) = 4!*(44-4)
961 (4) = ((gamma(gamma(4))+4)/4)^sqrt(4)
962 (4) = (4+4)*gamma(gamma(4))+sqrt(4)
963 (4) = root(.4,4/.4~)+gamma(4)!
964 (4) = (4+4)*gamma(gamma(4))+4
965 (6) = (square(44)-gamma(4))/sqrt(4)
966 (4) = (4+4)*gamma(gamma(4))+gamma(4)
967 (6) = (square(44)-sqrt(4))/sqrt(4)
968 (0) = sqrt(44^4/4)
969 (4) = (gamma(4)!+gamma(4))/sqrt(.4~)-gamma(gamma(4))
970 (4) = 4^4-gamma(4)+gamma(4)!
971 (5) = (gamma(sqrt(4))+.4%)/.4%+gamma(4)!
972 (3) = 4*root(.4,4/.4~)
973 (6) = square(square(4))+gamma(4)!-sqrt(4/.4~)
974 (4) = gamma(4)!+4^4-sqrt(4)
975 (2) = (sqrt(4)+4!)!/4!!/sqrt(.4~)
976 (0) = (4!/4)!+4^4
977 (4) = gamma(sqrt(4))+gamma(4)!+4^4
978 (4) = gamma(4)!+sqrt(4)+4^4
979 (6) = root(sqrt(4%),4)-gamma(4)!/square(4)
980 (4) = gamma(4)!+4+4^4
981 (4) = (gamma(gamma(4))-4)/.4~+gamma(4)!
982 (4) = gamma(4)!+gamma(4)+4^4
983 (6) = (4-.4%)/.4%-square(4)
984 (0) = sqrt(4!*((4+4)!+4!))
985 (5) = 4/.4%-gamma(4)/.4
986 (4) = gamma(gamma(4))/.4~+gamma(4)!-4
987 (6) = root(sqrt(4%),4)-gamma(sqrt(4))-square(gamma(4))
988 (4) = gamma(gamma(4))/.4~+gamma(4)!-sqrt(4)
989 (4) = (gamma(gamma(4))-.4~)/.4~+gamma(4)!
990 (4) = gamma(4!/sqrt(4))/(4+4)!
991 (4) = (gamma(gamma(4))+.4~)/.4~+gamma(4)!
992 (4) = (4+4)*(gamma(gamma(4))+4)
993 (5) = (4-.4%)/.4%-gamma(4)
994 (4) = gamma(gamma(4))/.4~+gamma(4)!+4
995 (5) = (4-.4%)/.4%-4
996 (0) = sqrt(sqrt(sqrt((4/.4)^4!)))-4
997 (5) = 4/.4%-sqrt(4/.4~)
998 (0) = sqrt(sqrt(sqrt((4/.4)^4!)))-sqrt(4)
999 (2) = 444/.4~
1000 (0) = 4*4^4-4!

HypnoticPoo

Singapore291 Posts

August 27 2008 07:05 GMT

#24

HAHA the cool thing is that the video is from Singapore, can see our MRT and the 4D lottery, really popular with Singaporeans, we take note of any funny number or w/e just for lottery

XCetron

5225 Posts

August 27 2008 10:01 GMT

#25

This is just common binary principle isnt it.

micronesia

United States24604 Posts

August 27 2008 10:24 GMT

#26

Yay thunk also wins.

On August 27 2008 16:05 HypnoticPoo wrote:
HAHA the cool thing is that the video is from Singapore, can see our MRT and the 4D lottery, really popular with Singaporeans, we take note of any funny number or w/e just for lottery

Haha yeah. IIRC the video was a runner up in a short film contest in Singapore.

On August 27 2008 19:01 XCetron wrote:
This is just common binary principle isnt it.

That's what she said.

Normal

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