sod(N) = 100, and sod(44*N) = 800
are satisfied simultaneously.
Determine sod(3*N), providing valid reasoning for your answer.
Notes:
i) sod(m) denotes the sum of the digits of m, where m is a positive integer.
ii) Computer program and spreadsheet assisted methodologies are welcome, but an analytical solution is preferred.
iii) Adapted from a problem which appeared at a Russian Mathematical Olympiad.
