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 substring 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.
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
The six numbers with the given property sum to
16695334890

Posted by Jer
on 20170727 12:43:06 