Four Nines Puzzle

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I'm not sure if this is the right place to put this, but here goes. I got bored one day However, it's easier than it looks. You can put this on the puzzle page if you want along with the Rubik's cube (which I never solved...)

FOUR NINES PUZZLE

Using EXACTLY four nines and any other mathematical symbols (but no words), construct all numbers between 1 and 132. Example:

0 = 99-99
_
You may assume that .9 = 1, and you cannot turn a 9 upside down and call it a 6.

I found that there's an easy way to get most of them. However, ALL are possible. The hardest ones by far are the numbers between 65 and 70, inclusive. 69 is absolute hell and requires a construction which is unique to that number.

Good luck!

ACG

Sorry about that: 68 is the really hard one, not 69.

ACG

One last thing: that .9 = 1 thing is supposed to have a bar over the 9. Yes, .9 bar: .99999...

ACG

The simplest I came up with:
68 = (sqrt 9)! ! / 9 - 9 - sqrt 9

Interesting page about this problem: http://www.magicdragon.com/EmeraldCity/ ... our9s.html

It isn't possible!! !

I swear!! !!

Ok so maybe I'm missing something blindingly obvious.

I shall just ahve to console myself in the knowledge that I CAN do the rubik cube..

it may take me 10 mins, but I can do it.!

Here's a hint (spoilers)






















Try to think of how many low numbers you can make with two nines. All you need are the factorial, root, parentheses, +, -, /, *, exponentiation, and bar symbols.

Then suppose you can make a larger number with two nines (say 81). You then can get: ...81-3, 81-2, 81-1, 81+0, 81+1, 81+2, 81+3...

So far I've been able to get:
SPOILER ALERT























1 = 99/99
2 = 9/9 + 9/9
3 = (9 + 9 + 9) / 9
4 = √9 + 9^(9-9)
6 = √9 + √9 + 9 - 9
7 = 9 - (9 + 9) / 9
9 = 9 + (9 - 9) × 9
10 = (99 - 9) / 9
12 = 9 + 9 - √9 - √9
18 = 9 + 9 + 9 - 9
20 = 99/9 + 9
36 = 9 + 9 + 9 + 9
81 = 91 - 9 - 9
98 = 99 - 9/9
99 = 99 + 9 - 9
100 = 99 + 9/9
102 = 99 + √9
111 = 999/9
117 = 99 + 9 + 9