Four Nines

[grandpascorpion]

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)!

[JuanTutors]

Originally Posted by grandpascorpion

111 = ((√9)!)! / (√9)! - (√9)! - (√9)

Wow .... how did you discover this one??

111 = 999/9

[cheesehead]

Originally Posted by petrw1

Factorial: √(9!) = 6

I think you meant:
Factorial: (√9)! = 6

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.

[cheesehead]

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.

[cheesehead]

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.

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.

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.

[Zeta-Flux]

43 = ((sqrt(9)! * sqrt(9)!)/9)sqrt(9)
(The last operation is concatenation.)

49 = ((sqrt(9)! * sqrt(9)!)/9)9

94 = 49 concatenation reversed

[Zeta-Flux]

52 = (concat(sqrt(9),9+sqrt(9)))/(sqrt(9)!)

[cheesehead]

Well, so much for the invisibility of concatenation.

[Uncwilly]

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.

[petrw1]

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

[grandpascorpion]

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)?