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.
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
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Posted by Jer
on 2017-07-27 12:43:06 |
hand solution
