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Thread: digits

  1. #1 digits 
    Forum Sophomore
    Join Date
    Feb 2008
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    what is the maximum number of times the digit 3 repeats itself in a number which is a multiple of 7


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  3. #2  
    Forum Professor serpicojr's Avatar
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    Jul 2007
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    Take any string of 3's (which I'll denote by 3...3). Append the digits 0 through 6 to the string:

    3...30
    3...31
    3...32
    3...33
    3...34
    3...35
    3...36

    Exactly one of these guys must be divisible by 7. So there is no maximum number of 3's you can have.


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  4. #3  
    Forum Ph.D.
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    Apr 2008
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    Any integer consisting of only 3’s, where the number of 3’s is divisible by 6, is divisible by 7:

    333 333
    333 333 333 333
    333 333 333 333 333 333
    333 333 333 333 333 333 333 333

    … etc
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