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parag1973
Posted: Sun Jun 29, 2008 5:59 am    Post subject: digits Reply with quote

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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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serpicojr
Posted: Sun Jun 29, 2008 8:34 am    Post subject: Reply with quote

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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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JaneBennet
Posted: Sun Jun 29, 2008 9:08 am    Post subject: Reply with quote

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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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