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Thread: This one might be tricky

  1. #1
    Feb 2008

    This one might be tricky

    This is for a game I play,

    you can take a "som" of a person, it gives you a number, but the number is not 100% accurate it can be off by +/- 45%, there is no way to tell how far off it is with just 1 number.

    You can take multiple "soms" to get 2, 3 or 4 numbers all off by different percents from the correct number.

    the numbers can be off by 1% 4% 18% etc. but can not be off by something like 1.34% or 6.542%. They are off by whole percents.

    The maximum error is 45%

    Using this I think it should be possible to make a formula to figure out the correct answer given 3-4 numbers.

    I wanted to work this into a spread sheet but I got a little stuck...

    Help please

    whoops this probably is in the wrong section, I am definitely in first year university
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  2. #2
    GAMMA Mathematics
    colby2152's Avatar
    Nov 2007
    Alexandria, VA
    Can you shed some light on the actual writing of the question? It seems a bit ambiguous to me.
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  3. #3
    Feb 2008
    managed to get a spreadsheet up that does it, had to use arrays so had to get a bit of help on the programming end of things,

    it ended up not being a math question at all really.

    i think it would be something like

    f(x)= x*b
    f(x)= x*a

    (a is a integer between +/- 1-45)
    (b is a int between +/- 1-45)

    solve for x, in some cases u needed a c, or even rarely a d. if b and a were equal ofc u get infinite results.

    it was for a game where you arent supposed to figure out the exact number, so there is some uncertainty but using this spread sheet
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  4. #4
    Mar 2008
    Let $\displaystyle n$ be the unknown number. Say the first trial gives the value $\displaystyle k$. Then we can conclude that $\displaystyle n$ is between $\displaystyle \frac{k}{1.45} \text{ and } \frac{k}{.45} $

    trial 2 gives a result of $\displaystyle j$. Again:
    $\displaystyle n$ is between $\displaystyle \frac{j}{1.45} \text{ and } \frac{j}{.45} $. since we have information from the previous round about the interval in which $\displaystyle n$ could be, intersect the two intervals.


    But will this always terminate with a conclusion "$\displaystyle n$ must be..."??
    No, since the number k could come up every single round and no new information is gained. If we require that a new number be given every single round then the worst case scenario is around $\displaystyle \frac{n}{.45}-\frac{n}{1.45} $ rounds, since every integer in the interval $\displaystyle [.45n,1.45n]$ might come up.

    An interesting question is, what is the expected number of steps required for you to be 10% or 50% or 95% sure of the number?
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