Themed Challenge 5 (Finn Hulse): Finn-umbers!

Logic Level 4

Finn Hulse is doodling in his notebook, and decides to coin a new term.

A three-digit number $$\overline{abc}$$, where $$a,b,c$$ are digits, is said to be a Finn-umber if it follows the following conditions:

1. $$\overline{ab}$$ is divisible by some natural number $$n$$, and $$\overline{bc}$$ is divisible by $$n$$

2. $$\overline{abc}$$ as a three digit number must not be divisble by $$n$$

Finn took two random Finn-umbers, $$x, y$$, and subtracted them, and found that the result itself was another Finn-umber, say $$z$$.

Now, find the sum of the maximum values of $$x$$ and $$y$$, which would give the least possible value of $$z$$.

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