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 Productive Numbers (Posted on 2013-05-26)
Find all possible 9-digit numbers using precisely nine distinct digits from 0 to 9 such that each pair of consecutive digits is the product of two single-digit numbers.

For example, 2 and 1 can appear next to each other since 3*7=21. However, 2 and 6 cannot appear next to each other since 26 is the product only of 2 and 13 (and 1 and 26), and each pair of factors contains a number that is not a single-digit number.

*** None of the 9-digit numbers can contain any leading zero.

 No Solution Yet Submitted by K Sengupta No Rating

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 re: spoiler #1 | Comment 2 of 6 |
(In reply to spoiler #1 by Ady TZIDON)

Indeed Ady has found the only such number that lacks any zeros within it 728163549. And the factorizations are:
8*9 4*7 9*9 2*8 7*9 5*7 6*9 7*7

 Posted by Charlie on 2013-05-26 12:48:16

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