Vocabulary - Tight Bound

The tight bound tracks whether you're still constrained by the upper limit $N$. If your first two digits match $N$'s first two digits exactly, you're "tight" and can't exceed $N$'s third digit. Example: $N = 325$. If you've placed $32$, you're tight. Your next digit can only be $0$-$5$.

But if you placed $31$, you're no longer tight. Your next digit can be $0$-$9$. Once you place a digit smaller than $N$'s corresponding digit, you become "loose" and stay loose forever. You can never exceed $N$ anymore, so all future digits are free.