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Changing Numbers To Prescribed Values Under Special Limitations

  1. Feb 9, 2013 #1
    x=1825+91/1217

    y=7+2/3

    z=1827+2/3

    Is there any way to turn x into z only using the first two terms, andor a constant, and the operators ' + ', ' - ', ' * ', ' / '.

    I know I can take ((x)-(x mod 10)) + y = z, but this uses a modulus.

    ... Basically the core of the question is can I change any number's last digit and its decimal value to something I decide by only using the number itself and the desired digit and decimal?

    I feel like splitting the numerator and denominator and running independent operations on each might be the way to go.
     
    Last edited: Feb 9, 2013
  2. jcsd
  3. Feb 9, 2013 #2

    mfb

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    Staff: Mentor

    1217x = 2221116
    3y = 23
    As those do not have a common divisor (apart from 1), you can find integers q,r, such that qx+ry=1. That can be written with a long series of "x+x+x+... -y-y-y-..." (or vice versa), of course, so you do not need q and r.
    In the same way, you can get 1820. Add y and you are done.

    ? If you can use the constant z/x, it is easy.
     
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