 mersenneforum.org M51 arithmetic
 Register FAQ Search Today's Posts Mark Forums Read  2019-01-17, 04:47   #67
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

11000100001112 Posts Quote:
 Originally Posted by uau for example 31415926 fails at 607 already.
666 = 3*1*4*1*5*(9+2)+6   2019-01-17, 05:18   #68
uau

Jan 2017

1708 Posts Quote:
 Originally Posted by retina 666 = 43112609 ??
((4*3+1/(1+2))*6+0)*9
Other "??" aren't possible.   2019-01-17, 05:26   #69
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

11000100001112 Posts Quote:
 Originally Posted by uau ((4*3+1/(1+2))*6+0)*9 Other "??" aren't possible.
I found another also

666 = 4*3*(1+1/2+6*(0+9))

Using the 1/2 was the key it seems. I couldn't find any without a fractional component.   2019-01-17, 05:36   #70
uau

Jan 2017

23×3×5 Posts Quote:
 Originally Posted by retina I couldn't find any without a fractional component.
I checked that on the computer with the program changed to reject some fractional results, and yes it's not possible without an intermediate fraction of either x/2 or x/3.   2019-01-17, 09:02 #71 retina Undefined   "The unspeakable one" Jun 2006 My evil lair 3·7·13·23 Posts I had to cheat 666 = 3*(0-(2+1))*(3-77) 666 = -(2+0-9)*(96+0-1)+1 666 = 3*(0-4+0-2+4*57)   2019-01-17, 14:32 #72 henryzz Just call me Henry   "David" Sep 2007 Cambridge (GMT/BST) 23·739 Posts Some more solutions for the last 4 digits: 11 = 9+(9-3)/3 12 = 9+9-3-3 13 = 9+(9+3)/3 15 = -9+9*3-3 17 = 9+9-3/3 18 = 9+9+3-3 19 = 9+9+3/3 I can't solve 14 or 16. I suspect they aren't possible. What do people think to allowing notation such as the following? 117 to 120 = 8*(2+5+8) - L4D[3 to 0] 121 to 133 = 8*(2+5+8) + L4D[1 to 13] It is fairly clear and saves a lot of typing and mistakes.   2019-01-17, 14:45   #73
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

3×7×13×23 Posts Quote:
 Originally Posted by henryzz Some more solutions for the last 4 digits: 11 = 9+(9-3)/3 12 = 9+9-3-3 13 = 9+(9+3)/3 15 = -9+9*3-3 17 = 9+9-3/3 18 = 9+9+3-3 19 = 9+9+3/3 I can't solve 14 or 16. I suspect they aren't possible. What do people think to allowing notation such as the following? 117 to 120 = 8*(2+5+8) - L4D[3 to 0] 121 to 133 = 8*(2+5+8) + L4D[1 to 13] It is fairly clear and saves a lot of typing and mistakes.
So with a stride of 27 (-13 to +13) we only need to find the first four digit values.

130 = (8+2)*(5+8)
144 = 8*(2*5+8)
160 = 8/(2/(5*8))
168 = (8*2+5)*8
192 = 8*(2-5)*8
208 = 8*2*(5+8)
<222 to 226 not covered>
240 = (8-2)*5*8
<254+ not covered>

So we can fill in the gaps:
222 = 8*2*(5/(8/(9*9/3))-3)
223 = 8+2*5*(8+9*9/(3+3)) -- Also can be 208+15
224 = 8*2*(5+8+9-(9-3/3))
225 = 8/(2/(5/(8/(9+9*3*3)))) -- I especially like this one with all the divisions, also can be 240-15
226 = 8*2*(5+8+9/(9-3/3))

Last fiddled with by retina on 2019-01-17 at 14:46   2019-01-17, 16:51 #74 retina Undefined   "The unspeakable one" Jun 2006 My evil lair 3×7×13×23 Posts With the following suffixes we can span a stride of 9 (-4 to +4) 0 = 9-3*3 1 = 9/3/3 2 = (9-3)/3 3 = 9-3-3 4 = (9+3)/3 And with the following prefixes we can cover 251 to 274 inclusive 255 = (8+2+5)*(8+9) 261 = (8*2+5+8)*9 264 = 8*(2+5*8-9) 268 = -8/(2/(5-8*9)) 270 = -(8+2-5*8)*9   2019-01-17, 17:23 #75 henryzz Just call me Henry   "David" Sep 2007 Cambridge (GMT/BST) 23·739 Posts Feel free to use the ones that we have >13 or >4. Any additions to those lists may turn out to be useful. If results could be posted using the notation I am using in the 1st post that would save me some time. I have added: 8 = 9-3/3 9 = 9+3-3 10 = 9+3/3 to the L3D list   2019-01-17, 17:37   #76
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

3×7×13×23 Posts Quote:
 Originally Posted by henryzz I have added: 8 = 9-3/3 9 = 9+3-3 10 = 9+3/3 to the L3D list
Also:

6 = 9/3+3   2019-01-17, 18:09 #77 retina Undefined   "The unspeakable one" Jun 2006 My evil lair 3·7·13·23 Posts No brackets required 275 = 8*2+5+8+9*9*3+3   Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post ewmayer Science & Technology 34 2015-10-03 01:31 science_man_88 science_man_88 11 2014-07-30 22:53 science_man_88 Miscellaneous Math 42 2011-07-26 02:02 mfgoode Puzzles 82 2007-05-02 08:13 R.D. Silverman Factoring 3 2006-06-05 23:49

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