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Thread: Long Division

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    Long Division

    This is an oldie I dug out from the dusty depths of the HD:

    The following problem was submitted to the American Mathematical Monthly by P.L. Chessin way back in 1954, well before the days of computers when desktop calculators weren't even as

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    Re: Long Division

    Even in the 21st century, it can still be solved with paper and pencil only.<pre><span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow> 80809
    --------
    124)10020316
    992
    ----
    1003
    992
    ----
    1116
    1116
    ----
    0</font color=yellow></span hi></pre>


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    Re: Long Division

    Correct, of course. Even checked it with my calculator. <img src=/S/grin.gif border=0 alt=grin width=15 height=15>
    When I revisited this puzzle, I gleaned essentially 3 pieces of information (other than those in the hint) and found them sufficient to solve it. Don't tell me... you probably did it with 2, or using some sort of sleight of Hans. <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

    Anyway, I find the puzzle to be one of the great classics.

    Alan

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    Re: Long Division

    <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>Depends on how you count the pieces of information. The starting point for me was that subtracting a multiple of the denominator from the first four digits of the numerator leaves only a two digit number. This pattern is repeated, and that leads to the solution.</font color=yellow></span hi>

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    Re: Long Division

    Interesting. We appear to have had totally different takes on it.
    <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>I started by noticing that 8 x divisor -> 3 digit number. This means last digit of quotient must be 9 (-> 4 digit number) and divisor must be < 125 (since 8 x 125 -> 4 digit number). This leaves only the first digit of the quotient, which must be < 9. A simple trial shows that 123 x 80809 -> 7 digit number. So does 124 x 70809. But the dividend has 8 digits, so 124 x 80809 is the only solution.</font color=yellow></span hi>

    Alan

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