Humphrey has a phone numberIt took me a couple hours to figure out, as I systematically plowed through a means of avoiding theabc-def-ghijsuch that each digit is unique. Furthermore, it holds the property such that:ais divisible by 1,abis divisible by 2,abcis divisible by 3, and so on, so thatabcdefghijis divisible by 10. What is the number?

*brute force*approach. Rather than sharing the answer, though, I thought I'd give the following hints, which might seem obvious, but are easily glossed over as you focus on finding the answer.

- The digit for
*a*and*i*don't matter since 1 divides all natural numbers and 1 + 2 + 3 + ... + 9 = 45 which is divisible by 9. - A number is divisible by 3 if the sum of its digits add up to a number divisible by 3.
- A number is divisible by 6 if it is divisible by both 2 and 3.
- A number is divisible by 4 if the last two digits form a number divisible by 4.
- A number is divisible by 8 if the last three digits form a number divisible by 8.

Happy hunting.

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