Question 94
a) Determine the number of digits of the product $111111 \cdot 1111111111$, where the first factor has 6 digits and the second has 10 digits.
b) The numbers $2^{2016}$ and $5^{2016}$ are written next to each other to form a single number $N$ whose number of digits is the sum of the numbers of digits of the two numbers. For example, if we did this with $2^{3}$ and $5^{3}$ we would obtain the number 8125, which has 4 digits. Determine the number of digits of $N$.
b) The numbers $2^{2016}$ and $5^{2016}$ are written next to each other to form a single number $N$ whose number of digits is the sum of the numbers of digits of the two numbers. For example, if we did this with $2^{3}$ and $5^{3}$ we would obtain the number 8125, which has 4 digits. Determine the number of digits of $N$.