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Sixes and Sevens (Posted on 2014-08-02) Difficulty: 3 of 5
Find the smallest positive integer multiple of 84 whose base ten representation uses only the two digits 6 and 7.

No Solution Yet Submitted by K Sengupta    
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Hints/Tips re: computer solution | Comment 3 of 4 |
(In reply to computer solution by Charlie)

Another pattern is to look for all numbers consisting of 3k sevens and any non-zero numer of sixes , terminating by 76 .- plus  few permutations to find (or exclude) divisibikity by 7


e,g.  3 sevens and 3 sixes: only six possibilities:

776676, 767676, 677676, 766776, 667776, 677676,

767676 is divisible by 7, snce 767-676=91=13*7


  Posted by Ady TZIDON on 2014-08-02 15:00:56
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