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 Staggered divisibility (Posted on 2013-09-16)
The number, 1406357289, is a pandigital number (i.e. containing all of the digits - 0 to 9 - once, in some order), but it also has a rather interesting sub-string divisibility property.
Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note the following:

d2d3d4=406 is divisible by 2
d3d4d5=063 is divisible by 3
d4d5d6=635 is divisible by 5
d5d6d7=357 is divisible by 7
d6d7d8=572 is divisible by 11
d7d8d9=728 is divisible by 13
d8d9d10=289 is divisible by 17

Find the sum of all pandigital numbers with this property.

Source: Euler Project.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 re: spoiler MODIFIED Comment 3 of 3 |
(In reply to spoiler by xdog)

missed  867  divisible by 17

....d8d9d10 is divisible by 17
Possibles are:
86_  ** none possible
90_  ** none possible
289
323  ** dupe digit

missed  867  divisible by 17, creating 2 more numbers

 Posted by Ady TZIDON on 2013-09-16 14:05:33

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