1992
Problem - 4174
The two-digit integers from $19$ to $92$ are written consecutively to form the large integer $$N=192021\cdots 909192$$
Suppose that the $3^k$ is the highest power of $3$ that is a factor of $N$. What is $k$.
Answer
1
The answer is $\boxed{1}$. We are going to show that $N$ is a multiple of $3$, but not a multiple of $9$. It can be computed that the sum of $N$'s digits is $705$. Then it is clear now that this conclusion holds because $S(N)\equiv 3\pmod{9}$.