Question 48
Given a positive integer $N$ (written in base 10), define its integer substrings to be integers that are equal to strings of one or more consecutive digits from $N$, including $N$ itself. For example, the integer substrings of 3208 are $3,2,0,8,32,20,320,208$, and 3208. (The substring 08 is omitted from this list because it is the same integer as the substring 8, which is already listed.)
What is the greatest integer $N$ such that no integer substring of $N$ is a multiple of 9? (Note: 0 is a multiple of 9.)
What is the greatest integer $N$ such that no integer substring of $N$ is a multiple of 9? (Note: 0 is a multiple of 9.)