Rules 2 and 4 are equivalent.
We need the number of 7's to be a multiple of three and the number 3's to be a multiple of 7 to satisfy rules 1, 2, 3, 5 and 6.
3333333777 is the smallest such number but does not fit rule 4.
Rearranging the digits a bit gives the smallest that does as 3333377733
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