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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