Question 45
Three not necessarily distinct positive integers between $1$ and $99$, inclusive, are written in a row on a blackboard. Then, the numbers, without including any leading zeros, are concatenated to form a new integer $N$. For example, if the integers written, in order, are $25$, $6$, and $12$, then $N=25612$ (and not $N=250612$). Determine the number of possible values of $N$.