Classic problem: Four 4's - Page 6

rogue · 2005-09-30, 01:00

Do you believe that there is a solution for all of these?

fetofs · 2005-09-30, 01:04

Quote:

Originally Posted by Ken_g6

Basically, that sentence allowing 4! and repeating decimals is gone in mine, and the ! key is allowed generally.

I think repeated decimals should be allowed, or else the book wouldn't claim solutions up to 130 (while there's no solution for 93 I have found on the net).

fetofs · 2005-09-30, 01:22

((4 - .4)^sq+4^sq)/.4^sq=181
((4+4!)^sq+4!)/4=202

Wacky · 2005-09-30, 01:37

176 = 4 * 44
172 = 4 * 44 - 4
180 = 4 * 44 + 4
200 = 4 * 44 + 4!
250 = 4sqsq - 4!/4

Ken_g6 · 2005-09-30, 03:15

Quote:

Originally Posted by rogue

Do you believe that there is a solution for all of these?

No. I rather doubt that many, if any, can be solved. But I thought that about 113, too.

fetofs: That's the first time I've seen a solution that produces, then subtracts away .4. I'll see if I can find any other uses for that.

And I never saw anything about repeating decimals until I searched the internet. But the book could be wrong.

cheesehead · 2005-09-30, 05:39

A few solutions in 3/4 time:

54 = 4!*4!^sq/4^sq[sup]sq[/sup]

58 = (4^sq[sup]sq[/sup]-4!)/4

102 = 4^sq[sup]sq[/sup]*.4-.4

166 = 4!/.4^sq+4^sq

196 = (4!+4)^sq/4

fetofs · 2005-09-30, 13:02

214=(4+4)^sq+4!/.4^sq
294=((4/.4)^sq-4^sq)^sq/4!
269=(.4+4^sq)^sq+.4^sq/4

grandpascorpion · 2005-09-30, 13:54

249 = (4!/.4(4))sq - 4!
209 = (4!/.4(4))sq - 4sq
221 = (4!/.4(4))sq -4
225 = (4!/.4(4))sq
229 = (4!/.4(4))sq + 4
241 = (4!/.4(4))sq + 4sq
249 = (4!/.4(4))sq + 4!

204 = (4!sq+4sqsq)/4-4
207 = (4!sq+4sqsq-4)/4
208 = (4!sq+4sqsq)/4
209 = (4!sq+4sqsq+4)/4
210 = (4!/.4+4!)/.4
212 = (4!sq+4sqsq)/4+4
216 = 4sqsq-4!-4sq
220 = 4sqsq -4sq -4sq-4

Most of the solutions near 256 are easy just use 256-x where x uses 3 4's.

Also Found a pretty one for 180

4! + 4! + 4!
-----------
.4

S80780 · 2005-09-30, 14:24

Quote:

Originally Posted by fetofs

And, impressingly enough: [snip]
4*(.4+4!)+.4=98

Sorry for the misinformation! Should've let the programme run over the complete range and not entering each unknown candidate seperately. You get a slipping one too easily.

Benjamin

grandpascorpion · 2005-09-30, 14:59

I dub fetofs the Four-Four King.

Ken_g6 · 2005-09-30, 15:17

Here are the ones Wacky listed as missing, that I've found. It takes a while to pull them out of the cross-linked Excel file I make them in. Groupings show how I got some of the numbers.

171 = ((4-4/4)^sq+4)^sq

175 = (4!+4)/.4^sq
179 = (4!+4)/.4^sq+4

144 = 4!^sq/4
168 = 4!^sq/4+4!
184 = 4!^sq/4+4!+4^sq

192 = 4^sq[sup]sq[/sup]-4^sq[sup]sq[/sup]/4
188 = 4^sq[sup]sq[/sup]-4^sq[sup]sq[/sup]/4-4

150 = 4!/.4^sq
174 = 4!/.4^sq+4!
190 = 4!/.4^sq+4!+4^sq

191 = (4!+4)/.4^sq+4^sq

193 = 4^sq[sup]sq[/sup]-(4^sq[sup]sq[/sup]-4)/4

196 = 4^sq[sup]sq[/sup]-4!/.4
195 = 4^sq[sup]sq[/sup]-(4!+.4)/.4

197 = 4^sq[sup]sq[/sup]-(4!-.4)/.4

198 = 4!/.4^sq+4!+4!

199 = (4!+4)/.4^sq+4!

200 = (4^sq+4^sq)/.4^sq
201 = (4^sq+4^sq+.4^sq)/.4^sq

204 = (4^sq+4^sq)/.4^sq+4

207 = 4^sq[sup]sq[/sup]-4/.4^sq-4!

208 = 4^sq[sup]sq[/sup]-4!-4!

209 = (4!/(4*.4))^sq-4^sq

100 = (4/.4)^sq
84 = (4/.4)^sq-4^sq
210 = ((4/.4)^sq-4^sq)/.4

212 = 4^sq[sup]sq[/sup]-44

231 = 4^sq[sup]sq[/sup]-4/.4^sq
215 = 4^sq[sup]sq[/sup]-4/.4^sq-4^sq

232 = 4^sq[sup]sq[/sup]-4!
216 = 4^sq[sup]sq[/sup]-4!-4^sq

219 = 4^sq[sup]sq[/sup]-(4!^sq+4^sq)/4^sq

220 = 4^sq[sup]sq[/sup]-4!^sq/4^sq

221 = (4!/(4*.4))^sq-4

222 = 4^sq[sup]sq[/sup]-4/.4-4!

224 = 4^sq[sup]sq[/sup]-4^sq-4^sq

225 = (4!/(4*.4))^sq

2005-09-30, 01:22	#58
fetofs Aug 2005 Brazil 2·181 Posts	((4 - .4)^sq+4^sq)/.4^sq=181 ((4+4!)^sq+4!)/4=202 Last fiddled with by fetofs on 2005-09-30 at 01:25

2005-09-30, 05:39	#61
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 1E0C₁₆ Posts	A few solutions in 3/4 time: 54 = 4!4!^sq/4^sq[sup]sq[/sup] 58 = (4^sq[sup]sq[/sup]-4!)/4 102 = 4^sq[sup]sq[/sup].4-.4 166 = 4!/.4^sq+4^sq 196 = (4!+4)^sq/4 Last fiddled with by cheesehead on 2005-09-30 at 05:48

2005-09-30, 13:02	#62
fetofs Aug 2005 Brazil 2×181 Posts	214=(4+4)^sq+4!/.4^sq 294=((4/.4)^sq-4^sq)^sq/4! 269=(.4+4^sq)^sq+.4^sq/4 Last fiddled with by Wacky on 2005-10-02 at 01:50 Reason: Removed List of Unsolved

2005-09-30, 13:54	#63
grandpascorpion Jan 2005 Transdniestr 503 Posts	15^2 based answers and more 249 = (4!/.4(4))sq - 4! 209 = (4!/.4(4))sq - 4sq 221 = (4!/.4(4))sq -4 225 = (4!/.4(4))sq 229 = (4!/.4(4))sq + 4 241 = (4!/.4(4))sq + 4sq 249 = (4!/.4(4))sq + 4! 204 = (4!sq+4sqsq)/4-4 207 = (4!sq+4sqsq-4)/4 208 = (4!sq+4sqsq)/4 209 = (4!sq+4sqsq+4)/4 210 = (4!/.4+4!)/.4 212 = (4!sq+4sqsq)/4+4 216 = 4sqsq-4!-4sq 220 = 4sqsq -4sq -4sq-4 Most of the solutions near 256 are easy just use 256-x where x uses 3 4's. Also Found a pretty one for 180 4! + 4! + 4! ----------- .4 Last fiddled with by grandpascorpion on 2005-09-30 at 14:00

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2005-09-30, 01:00	#56
rogue "Mark" Apr 2003 Between here and the 11×577 Posts	Do you believe that there is a solution for all of these?

2005-09-30, 01:37	#59
Wacky Jun 2003 The Texas Hill Country 441₁₆ Posts	176 = 4 * 44 172 = 4 * 44 - 4 180 = 4 * 44 + 4 200 = 4 * 44 + 4! 250 = 4sqsq - 4!/4

2005-09-30, 14:59	#65
grandpascorpion Jan 2005 Transdniestr 503₁₀ Posts	I dub fetofs the Four-Four King.

2005-09-30, 15:17	#66
Ken_g6 Jan 2005 Caught in a sieve 18B₁₆ Posts	Here are the ones Wacky listed as missing, that I've found. It takes a while to pull them out of the cross-linked Excel file I make them in. Groupings show how I got some of the numbers. 171 = ((4-4/4)^sq+4)^sq 175 = (4!+4)/.4^sq 179 = (4!+4)/.4^sq+4 144 = 4!^sq/4 168 = 4!^sq/4+4! 184 = 4!^sq/4+4!+4^sq 192 = 4^sq[sup]sq[/sup]-4^sq[sup]sq[/sup]/4 188 = 4^sq[sup]sq[/sup]-4^sq[sup]sq[/sup]/4-4 150 = 4!/.4^sq 174 = 4!/.4^sq+4! 190 = 4!/.4^sq+4!+4^sq 191 = (4!+4)/.4^sq+4^sq 193 = 4^sq[sup]sq[/sup]-(4^sq[sup]sq[/sup]-4)/4 196 = 4^sq[sup]sq[/sup]-4!/.4 195 = 4^sq[sup]sq[/sup]-(4!+.4)/.4 197 = 4^sq[sup]sq[/sup]-(4!-.4)/.4 198 = 4!/.4^sq+4!+4! 199 = (4!+4)/.4^sq+4! 200 = (4^sq+4^sq)/.4^sq 201 = (4^sq+4^sq+.4^sq)/.4^sq 204 = (4^sq+4^sq)/.4^sq+4 207 = 4^sq[sup]sq[/sup]-4/.4^sq-4! 208 = 4^sq[sup]sq[/sup]-4!-4! 209 = (4!/(4.4))^sq-4^sq 100 = (4/.4)^sq 84 = (4/.4)^sq-4^sq 210 = ((4/.4)^sq-4^sq)/.4 212 = 4^sq[sup]sq[/sup]-44 231 = 4^sq[sup]sq[/sup]-4/.4^sq 215 = 4^sq[sup]sq[/sup]-4/.4^sq-4^sq 232 = 4^sq[sup]sq[/sup]-4! 216 = 4^sq[sup]sq[/sup]-4!-4^sq 219 = 4^sq[sup]sq[/sup]-(4!^sq+4^sq)/4^sq 220 = 4^sq[sup]sq[/sup]-4!^sq/4^sq 221 = (4!/(4.4))^sq-4 222 = 4^sq[sup]sq[/sup]-4/.4-4! 224 = 4^sq[sup]sq[/sup]-4^sq-4^sq 225 = (4!/(4*.4))^sq