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  1. #1
    Silver Lounger
    Join Date
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    Divisibility Challenge

    Can you replace the missing digits in the number <font color=blue>789,XYZ</font color=blue> so that the resulting number is divisible by 7, 8 and 9? There's a catch: You cannot use a 7, 8 or a 9.
    - Ricky

  2. #2
    Plutonium Lounger
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    Mar 2002
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    Re: Divisibility Challenge

    <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>Divisible by 7, 8 and 9 implies divisible by 7*8*9 = 504. Now 789,000 / 504 = 1565.47..., so the first multiple of 504 between 789,000 and 790,000 is 1566*504 = 789,264. The next multiple would be 1567*504 = 789,768, but although that still begins with 789, it uses a 7 and 8. The next multiple is over 790,000. So the only solution is 789,264.</font color=yellow></span hi>

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