 mersenneforum.org Classic problem: Four 4's
 Register FAQ Search Today's Posts Mark Forums Read  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, 22:07 #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, 22:09 #47 cheesehead   "Richard B. Woods" Aug 2002 Wisconsin USA 22·3·641 Posts 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   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, 23:04 #49 grandpascorpion   Jan 2005 Transdniestr 503 Posts 161= 159 + 2, 164 = 4 * 41 161 = (4!sq + 4)/4 + 4sq 164 = 4*(4sq + .4)/.4   2005-09-29, 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 = (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   2005-09-29, 23:30   #51

"Richard B. Woods"
Aug 2002
Wisconsin USA

22×3×641 Posts 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   2005-09-29, 23:35   #52
fetofs

Aug 2005
Brazil

2×181 Posts 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    2005-09-30, 00:02 #53 cheesehead   "Richard B. Woods" Aug 2002 Wisconsin USA 22×3×641 Posts ... 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   2005-09-30, 00:12   #54
fetofs

Aug 2005
Brazil

1011010102 Posts 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.    2005-09-30, 00:18 #55 Ken_g6   Jan 2005 Caught in a sieve 5·79 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.   Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post davieddy PrimeNet 26 2011-06-13 09:38 davieddy PrimeNet 6 2009-10-04 08:33 ian209 Hardware 4 2006-02-18 19:52 fetofs Puzzles 7 2005-10-16 11:45 JuanTutors Puzzles 24 2005-08-28 23:46

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