Classic problem: Four 4's - Page 5

S80780 · 2005-09-29, 21:03

According to http://ourworld.compuserve.com/homep...enny/200Up.htm the remaining 4-4's-representations up to 160 must have at least one squaring operation.

Wacky · 2005-09-29, 22:07

83 = (4! -.4)/.4 + 4!

Added
162 = 4!/(.4)sq + 4sq - 4
170 = 4!/(.4)sq + 4sq + 4
178 = 4!/(.4)sq + 4! + 4
182 = 4!/(.4)sq + 4sq + 4sq
186 = 4!/(.4)sq
194 = 4!/(.4)sq + 44

cheesehead · 2005-09-29, 22:09

83 = (4!-.4)/.4+4!

165 = (4!-.4^sq)/(.4^sq)+4^sq

167 = (4!^sq-4)/4+4!
168 = 4!^sq/4+4!
169 = (4!^sq+4)/4+4!

173 = (4!-.4^sq)/(.4^sq)+4!

I thought someone earlier posted: 192 = 4!*4+4!*4

And we've been using: 576 = 4!sq

cheesehead · 2005-09-29, 22:13

174 = (4!)/(.4sq)+4!
175 = (4!+.4sq)/(.4sq)+4!

grandpascorpion · 2005-09-29, 23:04

161 = (4!sq + 4)/4 + 4sq
164 = 4*(4sq + .4)/.4

cheesehead · 2005-09-29, 23:08

Solutions with fewer 4's than on the last summary:

14 = 4/.4+4
14 = 4! -4/.4

22 = 4sq+4!/4

30 = 4!+4!/4

63 = (4^sqsq-4)/4

65 = (4^sqsq+4)/4

76 = (4/.4)^sq-4!

124 = (4/.4)^sq+4!

126 = 4!/(.4^sq)-4!

143 = (4!^sq-4)/4

146 = 4!/(.4^sq)-4

and a typo correction:

144 = 4!sq/4 + 4/4 should have been
145 = 4!sq/4 + 4/4

cheesehead · 2005-09-29, 23:30

Earlier, while under the influence of beer :-) , rogue posted several solutions in which 4^sqsq was erroneously evaluated to equal 64 instead of 256.

Quote:

Originally Posted by rogue

50 = 4sqsq - 4/.4 - 4
53 = 4sqsq - 44/4
54 = 4sqsq - 4/.4
55 = 4sqsq - (4 - 4/4)sq
57 = 4sqsq - (4!+4)/4
62 = 4sqsq - (4+4)/4
64 = 4sqsq
67 = 4sqsq + 4 - 4/4
69 = 4sqsq + 4 + 4/4
71 = 4sqsq + (4!+4)/4
73 = 4sqsq + (4 - 4/4)sq
74 = 4sqsq + 4/.4
75 = 4sqsq + 44/4
78 = 4sqsq + 4/.4 + 4
79 = 4sqsq + 4sq - 4/4
81 = 4sqsq + 4sq + 4/4
87 = 4sqsq + 4! - 4/4
88 = 4sqsq + 4!
89 = 4sqsq + 4! + 4/4
98 = 4sqsq + 4! + 4/.4

All that work by rogue can be salvaged by simply adding 192 to the left side of each of those equations:

242 = 4sqsq-4/.4-4
245 = 4sqsq-44/4
246 = 4sqsq-4/.4
247 = 4sqsq-(4-4/4)sq
249 = 4sqsq-(4!+4)/4
254 = 4sqsq-(4+4)/4
256 = 4sqsq
259 = 4sqsq+4-4/4
261 = 4sqsq+4+4/4
263 = 4sqsq+(4!+4)/4
265 = 4sqsq+(4-4/4)sq
266 = 4sqsq+4/.4
267 = 4sqsq+44/4
270 = 4sqsq+4/.4+4
271 = 4sqsq+4sq-4/4
273 = 4sqsq+4sq+4/4
279 = 4sqsq+4!-4/4
280 = 4sqsq+4!
281 = 4sqsq+4!+4/4
290 = 4sqsq+4!+4/.4

fetofs · 2005-09-29, 23:35

Quote:

Originally Posted by Wacky

These still need a solution
78
93
107
131
157

161-255

(0.4^sq+(4-.4)^sq)/0.4^sq=82
4+(4^sq-.4^sq)/.4^sq=103
4^sq+(4^sq-.4^sq)/.4^sq=115
4!+(4^sq-.4^sq)/.4^sq=123

And, impressingly enough:

Quote:

Originally Posted by S80780

According to http://ourworld.compuserve.com/homep...enny/200Up.htm the remaining 4-4's-representations up to 160 must have at least one squaring operation.

4*(.4+4!)+.4=98

cheesehead · 2005-09-30, 00:02

... and fetofs's solutions lead to:

99 = (4^sq-.4^sq)/.4^sq

101 = (4^sq+.4^sq)/.4^sq

... which lead to:

157 = 4^sqsq-(4^sq-.4^sq)/.4^sq

fetofs · 2005-09-30, 00:12

Quote:

Originally Posted by fetofs

Quote:

Originally Posted by Wacky

93
107
131

163
166
171
172

176
(and more)

78=4^sq[sup]sq[/sup]*.4-(.4+4!)

Working on 93.

Ken_g6 · 2005-09-30, 00:18

Well, I guess it's time to post solutions for a few you hadn't gotten earlier (I don't know if you've solved them yet:

78 = 4!*4!sq/4sqsq+4!
82 = (4sqsq-4!)/4+4!
83 = (4sq-.4sq)/.4sq-4sq
98 = (4sq-.4sq-.4sq)/.4sq
103= (4sq-.4sq)/.4sq+4
107= 4sqsq-(4!-.4sq)/.4sq
115= (4sq-.4sq)/.4sq+4sq
123= (4sq-.4sq)/.4sq+4!
131= 4sqsq-(4sq+4)/.4sq
157= 4sqsq-(4sq-.4sq)/.4sq

93 is the only one under 160 I haven't found. Between 160 and 300, I couldn't find the following 25 (yet):

163
177
181
183
185
187
189
202
203
205
206
211
213
214
217
218
223
237
243
269
283
287
294
295
298

Also, I found a copy of the problem that's apparently from an earlier edition of my book on this page. It's almost the same as mine, but his is copyright 1976 and mine is 1980. Basically, that sentence allowing 4! and repeating decimals is gone in mine, and the ! key is allowed generally.

2005-09-29, 22:07	#46
Wacky Jun 2003 The Texas Hill Country 3²·11² Posts	83 = (4! -.4)/.4 + 4! Added 162 = 4!/(.4)sq + 4sq - 4 170 = 4!/(.4)sq + 4sq + 4 178 = 4!/(.4)sq + 4! + 4 182 = 4!/(.4)sq + 4sq + 4sq 186 = 4!/(.4)sq 194 = 4!/(.4)sq + 44 Last fiddled with by Wacky on 2005-09-29 at 22:58

2005-09-29, 23:04	#49
grandpascorpion Jan 2005 Transdniestr 503 Posts	*161= 159 + 2, 164 = 4 41** 161 = (4!sq + 4)/4 + 4sq 164 = 4*(4sq + .4)/.4

2005-09-30, 00:02	#53
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 17014₈ Posts	... and fetofs's solutions lead to: 99 = (4^sq-.4^sq)/.4^sq 101 = (4^sq+.4^sq)/.4^sq ... which lead to: 157 = 4^sqsq-(4^sq-.4^sq)/.4^sq Last fiddled with by cheesehead on 2005-09-30 at 00:03

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2005-09-29, 21:03	#45
S80780 Jan 2003 far from M40 5³ Posts	According to http://ourworld.compuserve.com/homep...enny/200Up.htm the remaining 4-4's-representations up to 160 must have at least one squaring operation.

2005-09-29, 22:09	#47
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 2²×3×641 Posts	83 = (4!-.4)/.4+4! 165 = (4!-.4^sq)/(.4^sq)+4^sq 167 = (4!^sq-4)/4+4! 168 = 4!^sq/4+4! 169 = (4!^sq+4)/4+4! 173 = (4!-.4^sq)/(.4^sq)+4! I thought someone earlier posted: 192 = 4!4+4!4 And we've been using: 576 = 4!sq

2005-09-29, 22:13	#48
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 2²×3×641 Posts	174 = (4!)/(.4sq)+4! 175 = (4!+.4sq)/(.4sq)+4!

2005-09-29, 23:08	#50
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 7692₁₀ Posts	Solutions with fewer 4's than on the last summary: 14 = 4/.4+4 14 = 4! -4/.4 22 = 4sq+4!/4 30 = 4!+4!/4 63 = (4^sqsq-4)/4 65 = (4^sqsq+4)/4 76 = (4/.4)^sq-4! 124 = (4/.4)^sq+4! 126 = 4!/(.4^sq)-4! 143 = (4!^sq-4)/4 146 = 4!/(.4^sq)-4 and a typo correction: 144 = 4!sq/4 + 4/4 should have been 145 = 4!sq/4 + 4/4

2005-09-30, 00:18	#55
Ken_g6 Jan 2005 Caught in a sieve 110001011₂ Posts	Well, I guess it's time to post solutions for a few you hadn't gotten earlier (I don't know if you've solved them yet: 78 = 4!*4!sq/4sqsq+4! 82 = (4sqsq-4!)/4+4! 83 = (4sq-.4sq)/.4sq-4sq 98 = (4sq-.4sq-.4sq)/.4sq 103= (4sq-.4sq)/.4sq+4 107= 4sqsq-(4!-.4sq)/.4sq 115= (4sq-.4sq)/.4sq+4sq 123= (4sq-.4sq)/.4sq+4! 131= 4sqsq-(4sq+4)/.4sq 157= 4sqsq-(4sq-.4sq)/.4sq 93 is the only one under 160 I haven't found. Between 160 and 300, I couldn't find the following 25 (yet): 163 177 181 183 185 187 189 202 203 205 206 211 213 214 217 218 223 237 243 269 283 287 294 295 298 Also, I found a copy of the problem that's apparently from an earlier edition of my book on this page. It's almost the same as mine, but his is copyright 1976 and mine is 1980. Basically, that sentence allowing 4! and repeating decimals is gone in mine, and the ! key is allowed generally.