Find a way to write digits 1 through 9 in sequence, so that any two consecutive digits are divisible either by 7 or 13.

Question

Find a way to write the digits 1 through 9 in sequence, so that the numbers determined by any two consecutive digits are divisible either by 7 or by 13.

Answer 1

784913526

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78 84 49 91 13 35 52 26 are all divisible either by 7 or by 13
see picture below for calculation method and steps leading to given result. 7 was chosen as starting number as any 2-digit number divisible by 7 or 13 is not ending with 7 (except 77 which can't be included)

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red fonts indicate duplication of digits where caculation line ends