20070202, 17:44  #12 
Jan 2005
Transdniestr
503 Posts 
Thanks, Peter. The others stump me. Onwards and upwards!
102 = ((√9)!)! / (√9)!  9  9 103 = 104 = 99/.9  (√9)! 105 = ((√9)!)! / (√9)!  9  (√9)! 106 = 107 = ((√9)!)! /9 + (√9)^(√9) 108 = ((√9)!)! / (√9)!  (√9)!  (√9)! 109 = 99 + 9/.9 110 = ((√9)!)! / (√9)!  9/.9 111 = ((√9)!)! / (√9)!  (√9)!  (√9) 112 = ( ((√9)!)! + (√9)!) / (√9)! 9 113 = ( ((√9)!)! (√9)! ) / (√9)! (√9)! 114 = ((√9)!)! / (√9)!  √9  √9 115 = ( ((√9)!)! + (√9)!) / (√9)! (√9)! 116 = ( ((√9)!)! (√9)! ) / (√9)! (√9) 117 = ( ((√9)!)! 9  9) / (√9)! 118 = ( ((√9)!)! + (√9)!) / (√9)! (√9) 119 = ((√9)!)! / (√9)!  9/9 120 = ((√9)!)! / (√9)! + 9  9 121 = ((√9)!)! / (√9)! + 9/9 122 = ((√9)!)! / (√9)! + (√9)! / (√9) 123 = ( ((√9)!)! +9 + 9) / (√9)! 124 = ( ((√9)!)! + (√9)! ) / (√9)! +(√9) 125 = ( ((√9)!)!  (√9)!) / (√9)! +(√9)! 126 = ((√9)!)! / (√9)! + √9 + √9 127 = ( ((√9)!)! + (√9)! ) / (√9)! +(√9)! 128 = ( ((√9)!)!  (√9)!) / (√9)! +9 129 = ((√9)!)! / (√9)! + (√9)! + (√9) 130 = ((√9)!)! / (√9)! + 9/.9 131 = 132 = 133 = 134 = 135 = 99 + (√9)! *(√9)! 136 = ( ((√9)!)! + 9!/((√9)!)! ) /9 153 = 9 * (√9)! * (√9)  9 156 = 9 * (√9)! * (√9)  (√9)! 159 = 9 * (√9)! * (√9)  (√9) 161 = ( (√9)^((√9)!) + ((√9)!)! ) / 9 162 = 9*9* (√9)! / (√9) 165 = 9 * (√9)! * (√9) + (√9) 168 = 9 * (√9)! * (√9) + (√9)! Last fiddled with by grandpascorpion on 20070202 at 18:01 
20070203, 01:57  #13 
Mar 2004
509 Posts 

20070203, 02:08  #14  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
I think you meant:
Factorial: (√9)! = 6 Quote:
(√9)% = .03 I don't like using the percent operator because it's basically just a sneaky division by 100. Of course, the decimal point just sneaks in a division by 10, so, to me, the percent operator and decimal point ought to be either both excluded or both included. 

20070203, 02:42  #15 
"Richard B. Woods"
Aug 2002
Wisconsin USA
17014_{8} Posts 

20070203, 02:47  #16  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
21 = (((√9)!)*√9) + (√9)!  √9 has 17 operators, counting a pair of parentheses as 2, but not counting spaces. But none of the parentheses are essential if we assume √ has highest precedence, ! is next, * (and /) next, and +  lowest, so: 21 = √9! * √9 + √9!  √9 with 9 operators. Quote:
But if ^ has a precedence between √ and , then: 21 = √9 ^ √9  √9  √9 has 7 operators. If we define simpler as "using fewer operators", then the simpler 21 = 9 + 9 + 9/√9 has only 4 operators. Quote:
0 = 99  99 but concatenation is the only "invisible" operator, so 99  99 could be considered simpler than 9 + 9  9  9. Last fiddled with by cheesehead on 20070203 at 03:38 

20070203, 02:50  #17 
May 2003
7·13·17 Posts 
43 = ((sqrt(9)! * sqrt(9)!)/9)sqrt(9)
(The last operation is concatenation.) 49 = ((sqrt(9)! * sqrt(9)!)/9)9 94 = 49 concatenation reversed Last fiddled with by ZetaFlux on 20070203 at 02:54 
20070203, 02:59  #18 
May 2003
7×13×17 Posts 
52 = (concat(sqrt(9),9+sqrt(9)))/(sqrt(9)!)

20070203, 03:42  #19 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
Well, so much for the invisibility of concatenation.
Last fiddled with by cheesehead on 20070203 at 03:43 
20070203, 04:39  #20 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
254B_{16} Posts 

20070203, 04:55  #21 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
41·113 Posts 
In response to this and previous comments: It was somewhat arbitrary (and somewhat not) what operators I chose to include/exclude. Yes % as a sneaky way to divide by 100 is no more or less sneaky than allowing a decimal point as a sneaky way to divide by 10; I just chose NOT to use it .... well, honestly, it never occured to me to use it. It the raging masses think it should be included, fine with me....other than it changes the whole puzzle and grandpascorpion et al have done a very fine job without it. On the other hand if you want to exclude the decimal point it will only make the puzzle harder....and I think impossible for some numbers from 0 to 100.
As far as concat goes, I chose to limit that to the single digits 9, not the intermediate results of calculations ... again it changes the whole puzzle and I suspect makes it too much less challenging. Introducing (REVERSED) is very inventive but I suggest a big stretch .... also not necessary for 49 or 94. I guess I will simply end with saying I know all numbers from 0 to 100 are possible within the guidelines I proposed. And yes I meant: (√9)! = 6 
20070203, 06:02  #22 
Jan 2005
Transdniestr
503 Posts 
Hehe, there's a bunch based around 120 = 6! / 6. I just went through the different combinations. Definitely a flagrant violation of the KISS principle.
Peter, I'm very curious about the solutions to 43, 49, 52, 94; solutions that use the stipulated set of operators. Does anyone want to take a crack at the numbers > 100 missing soultions (in my list above)? Last fiddled with by grandpascorpion on 20070203 at 06:03 