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Math Help - Express the value 100 using only the digit 9

  1. #1
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    Express the value 100 using only the digit 9

    Express 100 using only 9s , addition, subtraction, multiplication, division, exponents, and parentheses. The 9s must appear alone, that is, no multi digit numbers are allowed.
    Thanks!
    ignore question in title.
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  2. #2
    Super Member Quacky's Avatar
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    Re: 9s must appear alone

    You can do this for any integer, just by having

    \frac{9}{9}+\frac{9}{9}+...

    Is there no other complication making this a challenge? Otherwise, 9\times 9+9 is already 90, and it isn't difficult to see how to proceed.

    Are we only allowed to perform each operation once?
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  3. #3
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    Re: 9s must appear alone

    (9+\frac{9}{9})^2

    edit: uses a 2, ignore :S...

    Was trying to use operations only once, you can make it:

    (9+\frac{9}{9})*(9+\frac{9}{9})
    Last edited by terrorsquid; November 20th 2011 at 02:57 PM.
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  4. #4
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    Re: 9s must appear alone

    hopfully this doesn't count as trivial but:
    \frac{9}{9} + \frac{9}{9} +.... = 1+1+....

    repeat 100 times.

    edit: didn't see previous identical reply
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  5. #5
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    Re: 9s must appear alone

    Quote Originally Posted by terrorsquid View Post
    (9+\frac{9}{9})^2
    that method uses a 2 ...
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  6. #6
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    Re: 9s must appear alone

    So don't need to use ALL of them? (9s, addition, subtraction, mult, division, exponents, AND parenthesis?... Thank you people!
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  7. #7
    Super Member Quacky's Avatar
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    Re: 9s must appear alone

    We don't know - that was my original point. The question, as it stands, doesn't imply that you do. Is that the exact wording of the question?
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  8. #8
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    Re: 9s must appear alone

    \left(\frac{9 \times 9}{9} \times \left(9 + \frac{9+9}{9}\right)\right) + \frac{9}{9}

    uses 9 9's

    99.999999999999...... uses an infinite number to get the job done (does that count?)
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  9. #9
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    Re: 9s must appear alone

    Quote Originally Posted by mmathh View Post
    So don't need to use ALL of them? (9s, addition, subtraction, mult, division, exponents, AND parenthesis?... Thank you people!
    Using all of them:

    (9\times9)+(\frac{9+9+9+9}{9}\times 9) -(9+9)+(\frac{9}{9})^9

    Post #9
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