Squaring is Daring (2)

Number Theory Level pending

If you haven't done the earlier Squaring and Daring challenge, do it now.

Squaring and Daring (1)

Now that you have experimented a bit with two-digit numbers, let's start looking at 3-digit numbers. But first we must make an important realization by asking a simple question:

What is the greatest number we are able to get if we start with a 3 digit number?

Well, an input of 999 would give the greatest possible output.

$$9^2$$ + $$9^2$$ + $$9^2$$ = $$81 * 3$$ = 243

Now it is up to you to continue. Will we see new "kinds" of sequences with 3-digit, 4-digit, 5-digit, n-digit numbers?

But I have a final question that you should be able to answer…