Four Nines

[alpertron]

192 = (sqrt(9)!/sqrt(9))^(sqrt(9)!)*3

[Mini-Geek]

Originally Posted by alpertron

192 = (sqrt(9)!/sqrt(9))^(sqrt(9)!)*3

Don't you mean 192 = (sqrt(9)!/sqrt(9))^(sqrt(9)!)*sqrt(9)?

[alpertron]

Yes. Anyway, since 3 = sqrt(9) and 6 = sqrt(9)! the expressions would be easier to understand by using those numbers.

For example:

192 = (6/3)^6 * 3

Another solution, this time with no percent operator:

141 = (sqrt(9)!/.9+9)*9. Edit: This is the third solution. In post #26 I put another solution without %

[alpertron]

167 = (9! / (sqrt(9)!)! - sqrt(9))/sqrt(9)
169 = (9! / (sqrt(9)!)! + sqrt(9))/sqrt(9)
170 = (9! / (sqrt(9)!)! + sqrt(9)!)/sqrt(9) (this time without %)
177 = (9! / (sqrt(9)!)!)/sqrt(9) + 9 (this time without %)

[grandpascorpion]

241 = (sqrt(9)!)! /sqrt(9) + 9/9
242 = (sqrt(9)!)! /sqrt(9) + sqrt(9)!/sqrt(9)
243 = ( (sqrt(9)!)! + sqrt(9)! + sqrt(9) ) / sqrt(9)
244 = ( (sqrt(9)!)! + sqrt(9)! + sqrt(9)! ) / sqrt(9)
245 = ( (sqrt(9)!)! + sqrt(9)! + 9 ) / sqrt(9)
246 = (sqrt(9)!)! /sqrt(9) + sqrt(9) + sqrt(9)
247 = ( (sqrt(9)!)! + sqrt(9) ) / sqrt(9) + sqrt(9)!
248 = ( (sqrt(9)!)! - sqrt(9) ) / sqrt(9) + 9
249 = (sqrt(9)!)! /sqrt(9) + sqrt(9)*sqrt(9)
250 = ( (sqrt(9)!)! + sqrt(9) ) / sqrt(9) + 9
251 = ( (sqrt(9)!)! + sqrt(9)! ) / sqrt(9) + 9
252 = ( (sqrt(9)!)! + 9) / sqrt(9) + 9


258 = ( (sqrt(9)!)! + sqrt(9)!* sqrt(9)!) / sqrt(9)
267 = ( (sqrt(9)!)! + 9*9) / sqrt(9)
270 = sqrt(9)!^sqrt(9) + 9 * sqrt(9)!
288 = 9!/(sqrt(9)!)!- sqrt(9)!^ sqrt(9)
291 = 99 * sqrt(9) - sqrt(9)!
294 = 99 * sqrt(9) - sqrt(9)
295 = sqrt(9)!^ sqrt(9) + 9*9
297 = 99 * 9 * sqrt(9)
300 = 99 * sqrt(9) + sqrt(9)
303 = 99 * sqrt(9) + sqrt(9)!
315 = sqrt(9)!^ sqrt(9) + 99

[alpertron]

Originally Posted by grandpascorpion

297 = 99 * 9 * sqrt(9)

I think you meant 297 = 99 * 9 / sqrt(9)
Also the expression for 295 is really 297.

[grandpascorpion]

Oops, you're correct.

254 = sqrt(9)! / (sqrt(9))% + 9 * sqrt(9)!
281 = sqrt(9)! / (sqrt(9))% + 9 * 9
298 = 9 / (sqrt(9))% - sqrt(9)!/sqrt(9)
299 = 9 / (sqrt(9))% - 9/9
301 = 9 / (sqrt(9))% + 9/9
302 = 9 / (sqrt(9))% + sqrt(9)!/sqrt(9)
306 = 9 / (sqrt(9))% + sqrt(9) + sqrt(9)
309 = 9 / (sqrt(9))% + sqrt(9) * sqrt(9)

[grandpascorpion]

273 = (sqrt(9)/9% - sqrt(9)) * 9
282 = 9/(sqrt(9))% - 9 -9
285 = 9 / (sqrt(9))% -9 -sqrt(9)!
290 = 9 / (sqrt(9))% - 9/.9
310 = 9 / (sqrt(9))% + 9/.9

[petrw1]

0 = 9 + 9 - 9 - 9
0 = 99 - 99
1 = 99/99
2 = 99/9 - 9
2 = 9/9 + 9/9
3 = 9/(√9) + 9 - 9
4 = 9/(√9) + 9/9
5 = √9 + √9 - 9/9
5 = 9/.9 * 9/.9
6 = √9 + √9 - 9 + 9
7 = 9 - √9 + 9/9
8 = 99/9 - √9
9 = (√9 * √9) + 9 - 9
9 = (√9)! + (√9)! + (√9)! - 9
10 = (√9 * √9) + 9/9
10 = 99 / 9.9
11 = 9 + (9 + 9)/9
12 = √9 + √9 + √9 + √9
13 = 9 + √9 + 9/9
14 = 99/9 + √9
15 = √9 * √9 + √9 + √9
16 = (√9)! + 9 + 9/9
17 = 9 + 9 - 9/9
18 = 9 + 9 + 9 - 9
19 = 9 + 9 + 9/9
20 = 99/9 + 9
21 = ((√9)!)*√9) + (√9)! - √9
21 = (√9)^(√9) - (√9) - (√9)
21 = √9 ^ √9 - √9 - √9
21 = √9! * √9 + √9! - √9
21 = 9 + 9 + 9/√9
22 = ((√9)! * (√9)!) - 9 -√9)
22 = 9/.9 + 9 + √9
23 = ( ((√9)!)^(√9)- 9)/9
24 = 9 + 9 + √9 + √9
25 = (√9)^(√9) - (√9)!/(√9)
26 = (√9)! * (√9)! - 9/.9
27 = 9 + 9 + (√9)! + √9
28 = (√9)^(√9) + 9/9
29 = (√9)^(√9) + (√9)!/(√9)
30 = 9 + 9 + (√9)! + (√9)!
31 = ( ((√9)!)^√9-9 ) / 9
32 = √ ( ((√9)!/ √9)^(9/.9) )
33 = 9/.9 * √9 + √9
33 = 9 + 9 + 9 + (√9)!
34 = (√9)! * (√9)! - (√9)!/(√9)
35 = (√9)! * (√9)! - 9/9
36 = 9 + 9 + 9 + 9
37 = (√9)! * (√9)! + 9/9
38 = (√9)! * (√9)! + (√9)!/(√9)
39 = 9/.9 * √9 + 9
40 = ((√9)!-9/9)!/√9
41 = (((√9)!)^√9) / 9 + 9
42 = (√9)! * (9 - (√9)!/(√9) )
43 = (((√9)!)! / (√9)! + 9) / √9
43 = ((√(9)! * √(9)!)/9)√(9)
44 = 9 * (√9)! - 9/.9
45 = 99 - 9 * (√9)!
46 = (√9)! * (√9)! + 9/.9
47 = 9! / (9*((√9)!)!) - 9
48 = (9 + (√9)!) * √9 + (√9)
49 = ((((√9)!)! / (√9)!) / √9) + 9
49 = ((√(9)! * √(9)!)/9)9
50 = 9! / (9*((√9)!)!) - (√9)!
51 = (9 + (√9)!) * √9 + (√9)!
52 = 9 * (√9)! - ((√9)! / √9)
53 = 9! / (9*((√9)!)!) - √9
54 = (9 + (√9)!) * √9 + 9
55 = ((√9)!/(√9))^((√9)!) - 9
56 = (9-9/9)! / ((√9)!)!)
57 = (9 + 9/.9) * √9
58 = ((√9)!/(√9))^((√9)!) - (√9)!
59 = 9! / (9*((√9)!)!) +√9
60 = (√9 + √9)*9/.9
61 = ((√9)!/(√9))^((√9)!) - √9
62 = 9! / (9*((√9)!)!) +(√9)!
63 = 99 - (√9)! * (√9)!
64 = (√9 + 9/9)^(√9)
64 = (√9 - 9/9) ^ ( (√9)!)
64 = (√9 - 9/9) ^ ( (√9)!)
65 = 9! / (9*((√9)!)!) +9
66 = (√9)! * (9 + (√9)!/(√9) )
67 = ((√9)!/(√9))^((√9)!) + √9
68 = ((√9)!)!/9 - 9 - (√9)
69 = (√9)!*9/.9 + 9
70 = ((√9)!/(√9))^((√9)!) + (√9)!
71 = 9*9 - 9/.9
72 = 99 - (√9) * 9
73 = ((√9)!/(√9))^((√9)!) + 9
74 = ( ((√9)!)! - 9*(√9)! )/9
75 = ( ((√9)!)! + 9)/9 - (√9)!
76 = ( ((√9)!)! - (√9)!*(√9)! )/9
77 = ( ((√9)!)! - (√9)^ (√9) )/9
78 = ( ((√9)!)! + 9)/9 - (√9)
79 = 9*9 - (√9)!/(√9)
80 = 9*9 - 9/9
81 = 99 -9 -9
81 = 9 * 9 + 9 - 9
81 = (√9)^(√9+9/9)
82 = 9*9 + 9/9
83 = 9*9 + (√9)!/(√9)
84 = 99 -(√9)! -9
85 = ( ((√9)!)! - 9)/9 + (√9)!
86 = ( ((√9)!)! + 9*(√9)! )/9
87 = 99 -(√9)! -(√9)!
88 = ( ((√9)!)! - 9)/9 + 9
89 = 99 - 9/.9
90 = 99 - √9 - (√9)!
91 = 9*9 + 9/.9
92 = ((√9)!)!/9 + 9 + √9
93 = 99- √9 - √9
94 = (√9!/.9+9) * √9!
94 = 9/9% - √(9) - √(9)
94 = 99-(√9)!+.9~
95 = ((√9)!)!/9 + 9 + (√9)!
96 = 99 + √9 - (√9)!
96 = 99-9/√9
97 = 99 - (√9)!/(√9)
98 = 99 - 9/9
99 = 99 + 9 - 9
100 = 99 + 9/9
100 = 9/.9 * 9/.9
101 = 99/.9 - 9
102 = ((√9)!)! / (√9)! - 9 - 9
103 = 9/9% + 9/√(9)
104 = 99/.9 - (√9)!
105 = ((√9)!)! / (√9)! - 9 - (√9)!
106 = 9/9% + √(9) + √(9)
107 = ((√9)!)! /9 + (√9)^(√9)
108 = ((√9)!)! / (√9)! - (√9)! - (√9)!
109 = 99 + 9/.9
110 = ((√9)!)! / (√9)! - 9/.9
111 = ((√9)!)! / (√9)! - (√9)! - (√9)
111 = 999/9
112 = ( ((√9)!)! + (√9)!) / (√9)! -9
113 = ( ((√9)!)! -(√9)! ) / (√9)! -(√9)!
114 = ((√9)!)! / (√9)! - √9 - √9
115 = ( ((√9)!)! + (√9)!) / (√9)! -(√9)!
116 = ( ((√9)!)! -(√9)! ) / (√9)! -(√9)
117 = ( ((√9)!)! -9 - 9) / (√9)!
118 = ( ((√9)!)! + (√9)!) / (√9)! -(√9)
119 = ((√9)!)! / (√9)! - 9/9
120 = ((√9)!)! / (√9)! + 9 - 9
121 = ((√9)!)! / (√9)! + 9/9
122 = ((√9)!)! / (√9)! + (√9)! / (√9)
123 = ( ((√9)!)! +9 + 9) / (√9)!
124 = ( ((√9)!)! + (√9)! ) / (√9)! +(√9)
125 = ( ((√9)!)! - (√9)!) / (√9)! +(√9)!
126 = ((√9)!)! / (√9)! + √9 + √9
127 = ( ((√9)!)! + (√9)! ) / (√9)! +(√9)!
128 = ( ((√9)!)! - (√9)!) / (√9)! +9
129 = ((√9)!)! / (√9)! + (√9)! + (√9)
130 = ((√9)!)! / (√9)! + 9/.9
131 =
132 = ((√9)!)! / (√9)! + 9 + √9
133 =
134 = (((√9)!)! / 9) + 9 * (√9)!
135 = 99 + (√9)! *(√9)!
136 = ( ((√9)!)! + 9!/((√9)!)! ) /9
138 = ((√9)!)! / (√9)! + 9 + 9
140 = 9/((√(9)!)%) - 9/.9
141 = ((√(9)!)!/√(9) - 99
141 = (√(9)!/.9+9)*9
141 = 9/((√(9)!)%) - √(9)! - √(9)
144 = ((9 + √(9))*(9 + √(9))
146 = (√(9)!)/((√(9))%) - 9 * √(9)!
147 = ((√9)!)! / (√9)! + (9 * √9)
148 = 9/((√(9)!)%) - √(9)!/√(9)
149 = 9/((√(9)!)%) - 9/9
150 = ((9*9)/9%)/√(9)!
151 = (((√(9)!)! + ((√(9)!)!)/9 -9
152 = 9/((√(9)!)%) + √(9)!/√(9)
153 = 9 * (√9)! * (√9) - 9
154 = (((√(9)!)! + ((√(9)!)!)/9 - √(9)!
155 = ?
156 = 9 * (√9)! * (√9) - (√9)!
157 = (((√(9)!)! + ((√(9)!)!)/9 - √(9)
158 = ?
159 = 9 * (√9)! * (√9) - (√9)
160 = ((√9)!)! * (√9)! / (9 * √9)
161 = ( (√9)^((√9)!) + ((√9)!)! ) / 9
162 = 9*9* (√9)! / (√9)
163 = (((√(9)!)! + ((√(9)!)!)/9 + √(9)
164 = √(9)!/√(9)% - √(9)!*√(9)!
165 = 9 * (√9)! * (√9) + (√9)
166 = (((√(9)!)! + ((√(9)!)!)/9 + √(9)!
167 = (9! / (√(9)!)! - √(9))/√(9)
168 = 9 * (√9)! * (√9) + (√9)!
169 = (9! / (√(9)!)! + √(9))/√(9)
170 = (√(9)!)/((√(9))%) - 9/(√(9%))
170 = (9! / (√(9)!)! + √(9)!)/√(9)
171 = 9*√(9)! * √(9) + 9
172 =
173 = (√(9)!)/((√(9))%) - √(9)^√(9)
174 = ((√9)!)! / (√9)! + 9 * (√9)!
175 =
176 =
177 = (9! / (√(9)!)!)/√(9) + 9
177 = 9/((√(9)!)%) + √(9)^√(9)
179 = ((√(9))!)!/9 + 99
180 = 99 + 9*9
181 = 9*9 + 9/9%
182 = (√(9)!)/((√(9))%) - 9 - 9
183 = √(9)!/√(9)%*.9 + 3
184 =
185 = (√(9)!)/((√(9))%) - 9 - √(9)!
186 = (√(9)!)!/(√(9) - 9*(√(9)!
187 =
188 = (√(9)!)/((√(9))%) - 9 - √(9)
189 = (√(9)!)^√(9) - 9*√(9)
190 = (√(9)!)/((√(9))%) - 9/.9
191 = (9+9)/9%-9
192 = (√(9)!/√(9))^(√(9)!)*3
192 = (√(9)!/√(9))^(√(9)!)*3
193 =
194 = (9+9)/9%-√(9)!
195 =
196 =
197 = (9+9)/9%-√(9)
198 = (√(9)!)^√(9) - √(9)!*√(9)
199 = 99 + 9/9%
200 = ((√9)!)! / (√9)! + ((√9)!)! / 9
201 = ((√9)!)! / (√9)! + 9 * 9
202 = √(9)!/√(9)% + √(9)!/√(9)
203 = (9+9)/9%+√(9)
204 = ((√(9)!)!/√(9) - √(9)! * √(9)!
204 = (√9)! ^ √9 - 9 - √9
205 =
206 = (9+9)/9%+√(9)!
207 = (√(9)!)^√(9) - √(9)*√(9)
208 = (√(9)!)! -(√(9)!/√(9))^9
209 = (9+9)/9%+9
210 = (√(9)!)^√(9) - √(9) - √(9)
211 =
212 = (√(9)!)/((√(9))%) + 9 + √(9)
213 = (√(9)!)^√(9) - 9/√(9)
214 = (√(9)!)^√(9) - √(9)!/√(9)
215 = (√(9)!)^√(9) - 9/9
216 = (√(9)!)^√(9) + 9 - 9
217 = (√(9)!)^√(9) + 9/9
218 = (√(9)!)^√(9) + √(9)!/√(9)
219 = (√(9)!)^√(9) + 9/√(9)
219 = 9/√(9)% - 9 *9
220 = ((√(9)!)!/√(9)! + 9/9%
220 = (√(9)!)! - (9 + √(9)!)/(√(9)%)
221 =
222 = (√(9)!)^√(9) + √(9) + √(9)
223 =
224 =
225 = (√(9)!)^√(9) + √(9) * √(9)
226 = (√(9)!)^√(9) + 9/.9
227 = (√(9)!)/((√(9))%) + √(9)^√(9)
228 = ((√(9)!)!/√(9) - 9 - √(9)
228 = (√9)! ^ √9 + 9 + √9
229 =
230 = ((√(9)!)!/√(9) - 9/.9
231 = ((√(9)!)!/√(9) - √(9) - √(9)!
231 = (√(9)!)!/√(9) -√(9) * √(9)
232 =
233 =
234 = ((√(9)!)!/√(9) - 9 + √(9)
234 = ((√(9)!)!-9-9)/√(9)
235 = (((√(9)!)! - 9 - √(9)!) / √(9)
236 = (((√(9)!)! - 9 - √(9)) / √(9)
236 = √(9)!/√(9)% + √(9)!*√(9)!
237 = ((√(9)!)!/√(9) - 9 / √(9)
237 = (√(9)!)!/√(9) - 9/√(9)
238 = (((√(9)!)! - 9 + √(9)) / √(9)
238 = (√(9)!)!/√(9) - √(9)!/√(9)
239 = ((√(9)!)!/√(9) - 9 / 9
239 = (√(9)!)!/√(9) - 9/9
240 = ((√(9)!)!/√(9) - 9 + 9
241 = (√(9)!)! /√(9) + 9/9
242 = (√(9)!)! /√(9) + √(9)!/√(9)
243 = ( (√(9)!)! + √(9)! + √(9) ) / √(9)
244 = ( (√(9)!)! + √(9)! + √(9)! ) / √(9)
245 = ( (√(9)!)! + √(9)! + 9 ) / √(9)
246 = (√(9)!)! /√(9) + √(9) + √(9)
247 = ( (√(9)!)! + √(9) ) / √(9) + √(9)!
248 = ( (√(9)!)! - √(9) ) / √(9) + 9
249 = (√(9)!)! /√(9) + √(9)*√(9)
250 = ( (√(9)!)! + √(9) ) / √(9) + 9
251 = ( (√(9)!)! + √(9)! ) / √(9) + 9
252 = ( (√(9)!)! + 9) / √(9) + 9
254 = √(9)! / (√(9))% + 9 * √(9)!
258 = ( (√(9)!)! + √(9)!* √(9)!) / √(9)
267 = ( (√(9)!)! + 9*9) / √(9)
270 = √(9)!^√(9) + 9 * √(9)!
273 = (√(9)/9% - √(9)) * 9
281 = √(9)! / (√(9))% + 9 * 9
282 = 9/(√(9))% - 9 -9
285 = 9 / (√(9))% -9 -√(9)!
288 = 9!/(√(9)!)!- √(9)!^ √(9)
290 = 9 / (√(9))% - 9/.9
291 = 99 * √(9) - √(9)!
294 = 99 * √(9) - √(9)
295 = √(9)!^ √(9) + 9*9
297 = 99 * 9 * √(9)
297 = 99 * 9 * √(9)
298 = 9 / (√(9))% - √(9)!/√(9)
299 = 9 / (√(9))% - 9/9
300 = 99 * √(9) + √(9)
301 = 9 / (√(9))% + 9/9
302 = 9 / (√(9))% + √(9)!/√(9)
303 = 99 * √(9) + √(9)!
306 = 9 / (√(9))% + √(9) + √(9)
309 = 9 / (√(9))% + √(9) * √(9)
310 = 9 / (√(9))% + 9/.9
315 = √(9)!^ √(9) + 99
6561 = 9 * 9 * 9 * 9
6561 = (√9)^(9-9/9)
8991 = 999 * 9
9801 = 99 * 99
9999 = 9999

[R. Gerbicz]

After my computer search: the first missing value is n=257; there is only 47 missing value for n<=1000, and 5237 values for n<=10000. See the attachment for the shortest form for n=0..10000.

[petrw1]

Originally Posted by R. Gerbicz

After my computer search: the first missing value is n=257; there is only 47 missing value for n<=1000, and 5237 values for n<=10000. See the attachment for the shortest form for n=0..10000.

COOL!
Is it easy to rerun with a small change...there was much debate about the % operator; quite a bit against it. Could you rerun your program without it and see how many we lose.

Thanks.