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The Four Fours challenge (math)

just making a list to help out a bit (correct it if its wrong): 1? = 1 2? = 3 3? = 6 4? = 10 5? = 15 6? = 21 7? = 28 8? = 36 9? = 45 10? = 55 11? = 66 12? = 78 13? = 91 14? = 105 15? = 120 16? = 136 17? = 153 18? = 171 19? = 190 20? = 210 21? = 231 22? = 253 23? = 276 24? = 300 25? = 325 26? = 351 27? = 378 28? = 406 29? = 435 30? = 465 31? = 496 32? = 528 edit: fixed

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Posted: 8/23/2005 10:49 PM
(Edited: 8/23/2005 10:58 PM)

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Dacicus

Editor, Player (69)

Joined: 6/22/2005
Posts: 1050

There's a formula for the triangular numbers, which is what you're writing out. It's: n? = n × (n + 1) / 2. 139 = ((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)?

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Posted: 8/23/2005 10:57 PM
(Edited: 8/23/2005 11:03 PM)

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nesrocks

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aparently, that you wrote is wrong? 16? = 144 right edit: oh you're right, fixed 16? = 136

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Posted: 8/23/2005 11:00 PM
(Edited: 8/23/2005 11:16 PM)

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Dacicus

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Joined: 6/22/2005
Posts: 1050

Actually, you wrote 13? incorrectly in your list, so everything after it is also wrong. 13? = 78 + 13 = 91

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Posted: 8/23/2005 11:10 PM

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nesrocks

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147 = { [ (4!)? - [(√4)? ]? } / √4 148 = (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)? ]? } / √4 154 = (4!)? / √4 + √4 + √4 155 = (4!)? / √4 + 4? / √4 156 = (4!)? / √4 + 4 + √4 157 = (4!)? / √4 + 4 + (√4)? 158 = (4!)? / √4 + 4 + 4

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Posted: 8/23/2005 11:15 PM

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Dacicus

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Joined: 6/22/2005
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159 = (4!)? / √4 + (√4)? × (√4)? 160 = (4!)? / √4 + (√4 + √4)? 161 = {(√4)? × [(√4)?]?}? - (√4 + √4)? 162 = {(√4)? × [(√4)?]?}? - (√4)? × (√4)? 163 = {(√4)? × [(√4)?]?}? - 4 - 4 164 = {(√4)? × [(√4)?]?}? - 4 - (√4)? 165 = {(√4)? × [(√4)?]?}? - 4 - √4 166 = {(√4)? × [(√4)?]?}? - √4 - (√4)? 167 = {(√4)? × [(√4)?]?}? - √4 - √4 168 = (4? × √4)? - {[(√4)?]?}? × √4 169 = {(√4)? × [(√4)?]?}? - 4 / √4 170 = {(√4)? × [(√4)?]?}? - 4 / 4 171 = {(√4)? × [(√4)?]?}? - 4 + 4 172 = {(√4)? × [(√4)?]?}? + 4 / 4 173 = {(√4)? × [(√4)?]?}? + 4 / √4

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Posted: 8/23/2005 11:25 PM

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nesrocks

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dont get too complicated there ;) 168 = 44 * 4 - [(√4)?]? 174 = 44 * 4 - √4

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Posted: 8/23/2005 11:37 PM

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Dacicus

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Joined: 6/22/2005
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175 = (4?)? + {(√4)? × [√4 + (√4)?]}?

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Posted: 8/23/2005 11:43 PM

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nesrocks

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wow that one was a trip 176 = {(√4)? * [(√4)?]?}? + 4? / √4 177 = {(√4)? * [(√4)?]?}? + (√4)? + (√4)? 178 = {(√4)? * [(√4)?]?}? + (√4)? + 4 179 = {(√4)? * [(√4)?]?}? + 4 + 4 180 = (4 * 4)? + 44 181 = {(√4)? * [(√4)?]?}? + (√4 + √4)? 182 = 44 * 4 + [(√4)?]? 183 = {(√4)? * [(√4)?]?}? + 4? + √4

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Posted: 8/24/2005 12:50 AM

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Itstoearly

Joined: 8/10/2004
Posts: 173
Location: Bethel, VT

FODA, do you happen to know how high you can go before you reach a number unable to be written with 4 4's?

Posted: 8/24/2005 12:54 AM

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nesrocks

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i have no idea, and we are gonna find out

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Posted: 8/24/2005 1:06 AM

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Gorash

Joined: 4/16/2005
Posts: 251

Funny thing :) 184 = {(4? x 4) + [(√4)?]?} x 4

Posted: 8/24/2005 1:30 AM
(Edited: 8/24/2005 2:57 AM)

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nesrocks

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185 = {(√4)? * [(√4)?]?}? + 4? + 4 186 = 44 * 4 + 4? 187 = {(√4)? * [(√4)?]?}? + 4 * 4 188 = [44 + (√4)? ] * 4 189 = {(√4)? * [(√4)?]?}? + 4! - [(√4)?]?

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Posted: 8/24/2005 2:26 AM

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Itstoearly

Joined: 8/10/2004
Posts: 173
Location: Bethel, VT

190 = [4? ^ (√4)] * √4 - 4?

Posted: 8/24/2005 2:27 AM

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VirtualAlex

Joined: 5/31/2004
Posts: 464
Location: Minnesota

Wow I don't know anything about math, but I am very interested in this.

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Posted: 8/24/2005 2:29 AM
(Edited: 8/24/2005 3:16 AM)

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Itstoearly

Joined: 8/10/2004
Posts: 173
Location: Bethel, VT

FODA wrote:

186 = 44 * 4 + 4!

Should be 4?, not 4! I think 191= ( ( ( √4)? )? )? + 44 - 4 192= (44 +4) *4 193= (((√4)?+ 4)?)? - 4? -4?

Posted: 8/24/2005 3:11 AM
(Edited: 8/24/2005 3:20 AM)

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nesrocks

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you 191 is wrong, "( ( ( ( √4)? )? )? )?" is not 151... its 231 so i think you meant 191 = (((( √4)? )? )? )? - 44 + 4 193 = (((( √4)? )? )? )? - 44 + ( ( √4)? )? 194 = (4? * 4?) * √4 - [( √4)? ]? 195 = {(√4)? * [(√4)?]?}? + (√4 + √4)! 196 = (4? * 4?) * √4 - 4 197 = (4? * 4?) * √4 - ( √4)? 198 = (4? * 4?) * √4 - √4 199 = (((( √4)? )? )? )? - 4! - 4 - 4 200 = 4? * 4? * (4 - √4) 201 = (((( √4)? )? )? )? - 4! - 4 - √4 202 = (((( √4)? )? )? )? - 4! - (√4)? - √4 203 = (((( √4)? )? )? )? - 4! - √4 - √4 204 = (((( √4)? )? )? )? - 4! - [√(4 - √4)]? 205 = (((( √4)? )? )? )? - 4! - 4 + √4 206 = (((( √4)? )? )? )? - 4! - 4/4 207 = (((( √4)? )? )? )? - 4! - 4 + 4 208 = (((( √4)? )? )? )? - 4! + 4 / 4 209 = (((( √4)? )? )? )? - 4! - √4 + 4 210 = (((( √4)? )? )? )? - 4! + [√(4 - √4)]? 211 = (((( √4)? )? )? )? - 4! + √4 + √4 212 = (((( √4)? )? )? )? - 4! + 4? / √4 213 = (((( √4)? )? )? )? - 4! + 4 + √4 214 = (((( √4)? )? )? )? - 4! + 4 + (√4)? 215 = (((( √4)? )? )? )? - 4! + 4 + 4

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Posted: 8/24/2005 3:14 AM

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Itstoearly

Joined: 8/10/2004
Posts: 173
Location: Bethel, VT

200 = 4? * 4? * (4/(√4))

Posted: 8/24/2005 3:36 AM

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Dacicus

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Joined: 6/22/2005
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216 = (4? × √4)? + (√4)? × √4 217 = (4? × √4)? + 4 + (√4)? 218 = (4? × √4)? + 4 + 4 219 = (4? × √4)? + (√4)? × (√4)? 220 = (4? × √4)? + (√4 + √4)? 221 = {(√4)? × [4 + (√4)?]}? - 4? 222 = (4? × √4)? + 4 × (√4)? 223 = [(4 +√4)?]? - 4 - 4 224 = [(4 +√4)?]? - (√4)? - 4 225 = [(√4)? × 4 + (√4)?] ^ √4 226 = [(4 +√4)?]? - (√4)? - √4 227 = [(4 +√4)?]? - √4 - √4 228 = ({[(√4)?]?}?)? - √4 - 4 / 4 229 = [(4 +√4)?]? - 4 / √4 230 = [(4 +√4)?]? - 4 / 4

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Posted: 8/24/2005 4:27 AM

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nesrocks

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231 = ({[(√4)?]?}?)? - √4 - √4 + 4 232 = ({[(√4)?]?}?)? - 4 / 4 + √4 233 = ({[(√4)?]?}?)? + (√4)? - 4 / 4 234 = ({[(√4)?]?}?)? + √4 + 4 / 4 235 = ({[(√4)?]?}?)? - √4 + √4 + 4 236 = ({[(√4)?]?}?)? + 4 + 4 / 4 237 = ({[(√4)?]?}?)? + √4 + √4 + √4 238 = ({[(√4)?]?}?)? + √4 + √4 + (√4)? 239 = ({[(√4)?]?}?)? + √4 + √4 + 4 240 = ({[(√4)?]?}?)? + √4 + (√4)? + 4 241 = ({[(√4)?]?}?)? + √4 + 4 + 4 242 = ({[(√4)?]?}?)? + (√4)? + 4 + 4 243 = ({[(√4)?]?}?)? + 4 + 4 + 4 244 = ({[(√4)?]?}?)? + 4? + [√(√4+√4)]? 245 = ({[(√4)?]?}?)? + 4? + √4 + √4 246 = ({[(√4)?]?}?)? + 4? + √4 + (√4)? 247 = ({[(√4)?]?}?)? + 4? + √4 + 4 248 = ({[(√4)?]?}?)? + 4? + (√4)? + 4 249 = ({[(√4)?]?}?)? + 4? + 4 + 4 all derived from 231 :P

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Posted: 8/24/2005 6:21 AM

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Dacicus

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Joined: 6/22/2005
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250 = (4? × √4)? + 4? × 4 251 = [(√4)? × 4 + 4?]? - √4 252 = (4? + √4) × (4 + √4)? 253 = {√4 × [4 + 4 + (√4)?]}? 254 = 4 ^ 4 - 4 / √4 255 = 4 ^ 4 - 4 / 4 256 = 4 × 4 × 4 × 4 257 = 4 ^ 4 + 4 / 4 258 = 4 ^ 4 + 4 / √4 259 = [(√4)? × 4 + 4?]? + [(√4)?]? 260 = 4 ^ 4 + √4 + √4 261 = 4 ^ 4 + √4 + (√4)? 262 = 4 ^ 4 + 4 + √4 263 = 4 ^ 4 + 4 + (√4)? 264 = 4 ^ 4 + 4 + 4 265 = 4 ^ 4 + (√4)? ^ √4 266 = 4 ^ 4 + (√4 + √4)?

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Posted: 8/24/2005 7:09 AM
(Edited: 8/24/2005 8:14 AM)

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Randil

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Joined: 4/20/2005
Posts: 2161
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What the... You did to 266 in one night!? That was really, really fast. Well, why not: 267 = 4!*4? + 4! + (√4)? 268 = 4!*4? + 4! + 4 269 = (4?*√4)? + (4?)? + 4 270 = ({[(√4)?]?}?)? + (4+4)? + (√4)? 271 = ({[(√4)?]?}?)? +4*(4?) 272 = 4^4 + 4*4 273 = [(4+√4)?+√4]? - (√4)? 274 = [(4+√4)?+√4]? - √4 275 = ({[(√(√4*√4))?]?}?)? + 44 276 = ((4+√4)?)? +4 -4 277 = 4^4 + (4+√4)? 278 = ({[(√4)?]?}?)? + (4?)? -4 -4 279 = ({[(√4)?]?}?)? + (4?)? -4 -(√4)? 280 = ({[(√4)?]?}?)? + (4?)? -4 -√4 281 = ({[(√4)?]?}?)? + (4?)?- (√4)? - √4 282 = ({[(√4)?]?}?)? + (4?)? -(√4*√4) 283 = ({[(√4)?]?}?)? + (4?)? - (√(√4*√4))? I'm going to school now, but I'll get back to doing this later today. BTW, thanks for finding out the ({[(√4)?]?}?)?, FODA, that helped a lot.

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Posted: 8/24/2005 8:12 AM

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