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Add'em all ! (Posted on 2017-07-27) Difficulty: 4 of 5
The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property:

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 0 to 9 pandigital numbers with this property.

See The Solution Submitted by Ady TZIDON    
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Solution hand solution Comment 3 of 3 |
I also worked by hand.  Fortunately my answer agrees with Charlie.

As xdog pointed out d6 has to be 5 or 0 but can't be 0.
Which makes d6d7d8 one of:
506, 517, 528, 539, 561, 572, 583, 594
tacking on d9 and d10 without repeating reduces this to
52867, 53901, 57289

working in the other direction d5 brings us down to two options:
952867, 357289
what's left are divisibilities for 3 and 2.  Taking each option separately.

952867 leaves digits 0134.  d3 is even and d3+d4 is divisible by 3.  Only 30 fits, leaving d1d2 as 14 or 41
1430952867
4130952867

357289 leaves digits 0146.  d3 is even and d3+d4 is divisible by 3.  Both 06 and 60 fit leaving d1d2 as 14 or 41 either way
1406357289
4106357289
1460357289
4160357289

The six numbers with the given property sum to
16695334890


  Posted by Jer on 2017-07-27 12:43:06
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