Sum of digits
Number Theory
Level
4
\[ \large N = 13 \times 17 \times 41 \times 829 \times 56659712633 \] It is know that \(N\) is an 18-digit number, with nine of the ten digits from 0 to 9 each appearing twice. Find the sum of the digits of \(N\).
Honor Bonus: Do it without calculating the product.
This problem is taken from the 7th Hong Kong Pui Ching Invitational Mathematics Competition, year 2008.
by
Daniel Turizo