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Four Nines Puzzle

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ACG
Raven
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16 Jan 2005, 9:21 am

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


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ACG
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16 Jan 2005, 9:23 am

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

ACG


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ACG
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16 Jan 2005, 9:25 am

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

ACG


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magic
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16 Jan 2005, 4:26 pm

ACG wrote:
Sorry about that: 68 is the really hard one

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



neotopian
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17 Jan 2005, 2:23 pm

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.!



ACG
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18 Jan 2005, 7:50 pm

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...


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Dan
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06 Feb 2005, 11:05 pm

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