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Old 2005-09-29, 21:03   #45
S80780
 
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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.
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Old 2005-09-29, 22:07   #46
Wacky
 
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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
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Old 2005-09-29, 22:09   #47
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"Richard B. Woods"
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83 = (4!-.4)/.4+4!

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

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

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

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

And we've been using: 576 = 4!sq
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Old 2005-09-29, 22:13   #48
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174 = (4!)/(.4sq)+4!
175 = (4!+.4sq)/(.4sq)+4!
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Old 2005-09-29, 23:04   #49
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Default 161= 159 + 2, 164 = 4 * 41

161 = (4!sq + 4)/4 + 4sq
164 = 4*(4sq + .4)/.4
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Old 2005-09-29, 23:08   #50
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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 = (4sqsq-4)/4

65 = (4sqsq+4)/4

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

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

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

143 = (4!sq-4)/4

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

and a typo correction:

144 = 4!sq/4 + 4/4 should have been
145 = 4!sq/4 + 4/4
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Old 2005-09-29, 23:30   #51
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Earlier, while under the influence of beer :-) , rogue posted several solutions in which 4sqsq 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
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Old 2005-09-29, 23:35   #52
fetofs
 
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Quote:
Originally Posted by Wacky
These still need a solution
78
93
107
131
157

161-255
(0.4sq+(4-.4)sq)/0.4sq=82
4+(4sq-.4sq)/.4sq=103
4sq+(4sq-.4sq)/.4sq=115
4!+(4sq-.4sq)/.4sq=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
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Old 2005-09-30, 00:02   #53
cheesehead
 
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... and fetofs's solutions lead to:

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

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

... which lead to:

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

Last fiddled with by cheesehead on 2005-09-30 at 00:03
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Old 2005-09-30, 00:12   #54
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Quote:
Originally Posted by fetofs
Quote:
Originally Posted by Wacky
93
107
131

163
166
171
172

176
(and more)
78=4sq[sup]sq[/sup]*.4-(.4+4!)

Working on 93.

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Old 2005-09-30, 00:18   #55
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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.
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