# Problem 413: One-child Numbers
We say that a d-digit positive number (no leading zeros) is a one-child
number if exactly one of its sub-strings is divisible by d. For example,
5671 is a 4-digit one-child number. Among all its sub-strings 5, 6, 7,
1, 56, 67, 71, 567, 671 and 5671, only 56 is divisible by 4. Similarly,
104 is a 3-digit one-child number because only 0 is divisible by 3.
1132451 is a 7-digit one-child number because only 245 is divisible by
7. Let F(N) be the number of the one-child numbers less than N. We can
verify that F(10) = 9, F(103) = 389 and F(107) = 277674. Find F(1019).