[Challenge] Find the numbers of this sum

Question

In a certain numeric base, something curious happens if you sum the same three-digit number three times:

ABC
ABC
ABC +
______
CCC

Consider that A, B and C are the digits of these numbers in that specific base.

Now, write a code able to answer these two questions:

1) Find numbers ABC and CCC for base 10, if possible.

2) Find numbers ABC and CCC for a base given by the user, if possible.

If it is not possible, show a message saying it is impossible. :(
Solutions must be non-trivial, that is: ABC and CCC must not equal zero.

All weapons welcome! Let's do this!!

EDIT:
I just wrote a code so you people can check your results.
https://code.sololearn.com/cwP2kkt0h2Eq/

Answer 1

My try (only first part):
https://code.sololearn.com/cST40F08sscS/#py

Answer 2

@pedro it is a very good Algorithms based Challenge.
Why Don't you make them Assignment.

What's your Opinion about Assignment and Answer it Here.
https://www.sololearn.com/discuss/1082512/?ref=app

Answer 3

https://code.sololearn.com/c2XGuPnw1z7d/?ref=app

Answer 4

@Vishal, that's a good idea! Thank you for the compliment.

Answer 5

Without program - in base 10:
185
185
185
-------
555
This is easily determined by a simple award: the last digit multiplied by 3 gave the result ending in it. This property is possessed by 0 and 5. Obviously, 0 is not good. Further similarly computes the remaining digits.

Answer 6

https://code.sololearn.com/crOO455N014S/?ref=app