3.1. Lisa drew graphs of all functions of the form $y=a x+b$, where $a$ and $b$ take all natural values from 1 to 100. How many of these graphs pass through the point $(3,333)$?
Answer: 23

Solution. We are looking for such $a$ and $b$ that $333=3a+b$. That is, $b=3(111-a)$. Therefore, $0<111-a \leqslant 33$, $78 \leqslant a$. There are exactly 23 such $a$ and for each of them, $b$ can be uniquely determined.