Problem 43: Sub-string divisibility
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.
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 numbers of all 0 to 9 pandigital numbers with this property.
Test
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