How to find all three-digit number which are divisible by a sum of specific digit groups explained below?
The original number should have only non-zero and non-repeating digits.
$301$ has a zero digit - cannot be used
$331$ does not have different digits - cannot be used
And the number should be divisible by two-digit group of its own digits, which are made by omitting one of the number's digits.
$785$ should be divisible by $78$, $75$, and $85$.
I have come just to this:
If the number is made of digits $a, b, c$ like this $[abc]$, the number should be divisible by
$(10a + b) + (10b + c) + (10a + c) = 20a + 11b + 2c$
But I am not sure how to find all of the suitable numbers.
Thanks a lot for your time!