March Break 2024 - Problem 9

A repdigit is defined as a positive integer which, when written in decimal form, only contains one distinct nonzero digit. For example, 33333 and 7 are repdigits, while 10433 and 998 are not. Emily is bored, so she decides to write down every repdigit. If Emily writes down the smallest repdigit that has not already been written every second, find the number of seconds it will take until Emily writes down a number that is divisible by 2024.