Digit Set - Walkthrough

Count numbers $\leq 321$ using digits $\{1, 3, 5\}$. Build digit by digit, tracking tightness. Position $0$ (hundreds): if tight, try $1$ and 3 (but not 5, since $5 > 3$). If $3$, stay tight. If $1$, become loose. Position $1$ (tens): if tight (started with $3$), try $1$ (becomes loose, since $1 < 2$). If loose, try all: $1$, $3$, $5$. Position $2$ (units): if tight, try $1$ (since $1 \leq 1$). If loose, try all. Count all valid paths.

Answer: numbers like $111$, $113$, $115$, 131, ..., $311$, $313$, $315$ that are $\leq 321$.