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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what is the maximum number of times the digit 3 repeats itself in a number which is a multiple of 7
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.
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