 mersenneforum.org Four Nines
 Register FAQ Search Today's Posts Mark Forums Read  2007-02-02, 17:44 #12 grandpascorpion   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 2007-02-02 at 18:01   2007-02-03, 01:57   #13
JuanTutors

Mar 2004

509 Posts Quote:
 Originally Posted by grandpascorpion 111 = ((√9)!)! / (√9)! - (√9)! - (√9)
Wow .... how did you discover this one??

111 = 999/9   2007-02-03, 02:08   #14

"Richard B. Woods"
Aug 2002
Wisconsin USA

22×3×641 Posts Quote:
 Originally Posted by petrw1 Factorial: √(9!) = 6
I think you meant:
Factorial: (√9)! = 6

Quote:
 Other versions allow the percent operator (i.e. √9% = .3).
√(9%) = .3
(√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.   2007-02-03, 02:42   #15

"Richard B. Woods"
Aug 2002
Wisconsin USA

170148 Posts Quote:
 Originally Posted by Uncwilly ((√9)! * (√9)!) - 9 -√9) = 22
Maybe I'm misreading, but after removing the final, unmatched parenthesis I get (3! * 3!) - 9 - 3 = 24. I don't see how to produce 22 by just changing parentheses.   2007-02-03, 02:47   #16

"Richard B. Woods"
Aug 2002
Wisconsin USA

22·3·641 Posts Quote:
 21 = ((√9)!)*√9) + (√9)! - √9
... has unbalanced parentheses, but with addition of one paren on the left:

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:
 21 = (√9)^(√9) - (√9) - (√9)
... has 15 operators.

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 = 9 + 9 - 9 - 9
... has the minimum of 3 operators, as does:

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 2007-02-03 at 03:38   2007-02-03, 02:50 #17 Zeta-Flux   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 Zeta-Flux on 2007-02-03 at 02:54   2007-02-03, 02:59 #18 Zeta-Flux   May 2003 7×13×17 Posts 52 = (concat(sqrt(9),9+sqrt(9)))/(sqrt(9)!)   2007-02-03, 03:42 #19 cheesehead   "Richard B. Woods" Aug 2002 Wisconsin USA 22×3×641 Posts Well, so much for the invisibility of concatenation. Last fiddled with by cheesehead on 2007-02-03 at 03:43   2007-02-03, 04:39   #20
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

254B16 Posts Quote:
 Originally Posted by cheesehead Maybe I'm misreading, but after removing the final, unmatched parenthesis I get (3! * 3!) - 9 - 3 = 24. I don't see how to produce 22 by just changing parentheses.
Well I can't say what I was thinking.   2007-02-03, 04:55   #21
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

41·113 Posts Quote:
 Originally Posted by Zeta-Flux 52 = (concat(sqrt(9),9+sqrt(9)))/(sqrt(9)!)
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   2007-02-03, 06:02   #22
grandpascorpion

Jan 2005
Transdniestr

503 Posts Quote:
 Originally Posted by dominicanpapi82 Wow .... how did you discover this one?? 111 = 999/9
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 2007-02-03 at 06:03   Thread Tools Show Printable Version Email this Page

All times are UTC. The time now is 06:49.

Fri May 7 06:49:22 UTC 2021 up 29 days, 1:30, 0 users, load averages: 2.72, 2.58, 2.38