Four Nines - Page 4

petrw1 · 2007-02-05, 19:28

94 = (√9!/.9+9) * √9!

Mini-Geek · 2007-02-05, 21:33

a few slightly out of order ones:
6561 = 9 * 9 * 9 * 9
8991 = 999 * 9
9801 = 99 * 99
9999 = 9999

petrw1 · 2007-02-05, 21:58

Speaking of "out of order" solutions...how about:

9!^9!^9!^9! = <overflow>

9!!^9!!^9!!^9!! = <TILT!>

Mini-Geek · 2007-02-06, 02:28

$\infty$ = 9~^9~^9~^9~

alpertron · 2007-02-06, 02:35

Quote:

Originally Posted by Mini-Geek

$\infty$ = 9~^9~^9~^9~

$\large \infty = \frac{9+9}{9-9}$

Sorry, I couldn't resist.

Mini-Geek · 2007-02-06, 02:49

Quote:

Originally Posted by alpertron

$\large \infty = \frac{9+9}{9-9}$

Sorry, I couldn't resist.

That doesn't equal infinity, it obviously equals Nullity.

(in case your sarcasm detector's broken, yes, I'm being sarcastic and I don't think Nullity is real)

alpertron · 2007-02-06, 12:20

Quote:

Originally Posted by Mini-Geek

That doesn't equal infinity, it obviously equals Nullity.

(in case your sarcasm detector's broken, yes, I'm being sarcastic and I don't think Nullity is real)

According to that article the nullity is 0/0 which is different of what I expressed above.

alpertron · 2007-02-06, 13:11

Since the expression 9~ is nonsense, I will define it as 10ⁿ-1 and also I define .9~ as (10ⁿ-1)/10ⁿ. Then we take the limit of the entire expression for n -> inf.

With this definition we can find the values of e and $\pi$ with just four nines.

$\large e = \left(\frac{9\~+.9\~}{9\~}\right)^{9\~}$

$\pi$ is the imaginary part of:

$\large \sqrt{9\~} (-.9\~)^{\frac{\sqrt{9\~}}{9\~}}$

grandpascorpion · 2007-02-06, 16:07

208 = (sqrt(9)!)! -(sqrt(9)!/sqrt(9))^9
219 = 9/sqrt(9)% - 9 *9
220 = (sqrt(9)!)! - (9 + sqrt(9)!)/(sqrt(9)%) : 2nd solution
231 = (sqrt(9)!)!/sqrt(9) -sqrt(9) * sqrt(9)
234 = ((sqrt(9)!)!-9-9)/sqrt(9)
237 = (sqrt(9)!)!/sqrt(9) - 9/sqrt(9)
238 = (sqrt(9)!)!/sqrt(9) - sqrt(9)!/sqrt(9)
239 = (sqrt(9)!)!/sqrt(9) - 9/9

Any more solutions under 240? (Preferably where no additional operators (like %) are used)

131 = ?
133 = ?
137 = ?
139 = ?
142-145 = ?
155 = ?
158 = ?
164 = ?
167 = ?
169 = ?
172 = ?
175 = ?
176 = ?
178 = ?
183= ?
184 = ?
187 = ?
192= ?
193 = ?
195 = ?
196 = ?
202 = ?
204 = ?
205 = ?
211 = ?
221 = ?
223 = ?
224 = ?
228 = ?
229 = ?
232 = ?
233 = ?
235 = ?
236 = ?

alpertron · 2007-02-06, 19:14

164 = sqrt(9)!/sqrt(9)% - sqrt(9)!*sqrt(9)!
183 = sqrt(9)!/sqrt(9)%*.9 + 3
202 = sqrt(9)!/sqrt(9)% + sqrt(9)!/sqrt(9)
236 = sqrt(9)!/sqrt(9)% + sqrt(9)!*sqrt(9)!, but you skipped my solution without % on post #26.

Andi47 · 2007-02-06, 20:24

204 = (√9)! ^ √9 - 9 - √9 (Alpertron has given another solution above)
228 = (√9)! ^ √9 + 9 + √9

2007-02-05, 19:28	#34
petrw1 1976 Toyota Corona years forever! "Wayne" Nov 2006 Saskatchewan, Canada 1001001000100₂ Posts	94....within my suggested operators.... 94 = (√9!/.9+9) * √9!

2007-02-06, 16:07	#42
grandpascorpion Jan 2005 Transdniestr 503 Posts	208 = (sqrt(9)!)! -(sqrt(9)!/sqrt(9))^9 219 = 9/sqrt(9)% - 9 9 220 = (sqrt(9)!)! - (9 + sqrt(9)!)/(sqrt(9)%) : 2nd solution 231 = (sqrt(9)!)!/sqrt(9) -sqrt(9) sqrt(9) 234 = ((sqrt(9)!)!-9-9)/sqrt(9) 237 = (sqrt(9)!)!/sqrt(9) - 9/sqrt(9) 238 = (sqrt(9)!)!/sqrt(9) - sqrt(9)!/sqrt(9) 239 = (sqrt(9)!)!/sqrt(9) - 9/9 Any more solutions under 240? (Preferably where no additional operators (like %) are used) 131 = ? 133 = ? 137 = ? 139 = ? 142-145 = ? 155 = ? 158 = ? 164 = ? 167 = ? 169 = ? 172 = ? 175 = ? 176 = ? 178 = ? 183= ? 184 = ? 187 = ? 192= ? 193 = ? 195 = ? 196 = ? 202 = ? 204 = ? 205 = ? 211 = ? 221 = ? 223 = ? 224 = ? 228 = ? 229 = ? 232 = ? 233 = ? 235 = ? 236 = ? Last fiddled with by grandpascorpion on 2007-02-06 at 16:50

2007-02-06, 19:14	#43
alpertron Aug 2002 Buenos Aires, Argentina 2·683 Posts	164 = sqrt(9)!/sqrt(9)% - sqrt(9)!sqrt(9)! 183 = sqrt(9)!/sqrt(9)%.9 + 3 202 = sqrt(9)!/sqrt(9)% + sqrt(9)!/sqrt(9) 236 = sqrt(9)!/sqrt(9)% + sqrt(9)!sqrt(9)!, but you skipped my solution without % on post #26. Last fiddled with by alpertron on 2007-02-06 at 19:24*

2007-02-06, 20:24	#44
Andi47 Oct 2004 Austria 2×17×73 Posts	204 = (√9)! ^ √9 - 9 - √9 (Alpertron has given another solution above) 228 = (√9)! ^ √9 + 9 + √9 Last fiddled with by Andi47 on 2007-02-06 at 20:30 Reason: 204

2007-02-05, 21:33	#35
Mini-Geek Account Deleted "Tim Sorbera" Aug 2006 San Antonio, TX USA 17×251 Posts	a few slightly out of order ones: 6561 = 9 * 9 * 9 * 9 8991 = 999 * 9 9801 = 99 * 99 9999 = 9999

2007-02-05, 21:58	#36
petrw1 1976 Toyota Corona years forever! "Wayne" Nov 2006 Saskatchewan, Canada 2²·7·167 Posts	Speaking of "out of order" solutions...how about: 9!^9!^9!^9! = <overflow> 9!!^9!!^9!!^9!! = <TILT!>

2007-02-06, 02:28	#37
Mini-Geek Account Deleted "Tim Sorbera" Aug 2006 San Antonio, TX USA 4267₁₀ Posts	$\infty$ = 9~^9~^9~^9~

2007-02-06, 13:11	#41
alpertron Aug 2002 Buenos Aires, Argentina 1366₁₀ Posts	Since the expression 9~ is nonsense, I will define it as 10ⁿ-1 and also I define .9~ as (10ⁿ-1)/10ⁿ. Then we take the limit of the entire expression for n -> inf. With this definition we can find the values of e and $\pi$ with just four nines. $\large e = \left(\frac{9\~+.9\~}{9\~}\right)^{9\~}$ $\pi$ is the imaginary part of: $\large \sqrt{9\~} (-.9\~)^{\frac{\sqrt{9\~}}{9\~}}$