Splitting and adding the numbers

Question

All the natural numbers from $1$ to $100$ are written adjacent to each other in a single row. Now, this is considered as a single number, $N$ with $192$ digits.
$N$ is then broken into two parts each part being considered to be a new number, by placing a single partition between any two consecutive digits of $N$ and the two numbers so obtained are added to form a new number $N1$.
Now, $N1$ is broken into two parts in a manner similar to that followed above for $N$ and the two numbers thus arrived at are again added to form another new number $N2$. This process is continued to arrive at $N3$, $N4$.... and so on till we finally get a single digit number $Nm$.
What is the value of $Nm$?

user2661923 · Answer

First of all, as suggested by the comment of астон вілла тереса лисбон, the problem would probably not have been posed if there was not a unique answer.
Hint: if you apply the rule of "casting out 9's", what will the final digit be, modulo 9?  If you can prove that it must be 0 mod 9, is that conclusive?
Addendum
It just occurred to me; suppose that casting out 9's indicates that the final digit is not congruent to 0 modulo 9.  For example, suppose that the final digit must be congruent to 5 modulo 9.  Would you then (still) be able to determine a unique answer?

Splitting and adding the numbers

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