1. Given points $A(0,4)$ and $B(4,0)$. If the parabola $y=x^{2}-m x+m+1$ intersects the line segment $A B$ (excluding endpoints $A$ and $B$) at two distinct points, then the range of values for $m$ is $\qquad$.
(1997, Shanghai High School Mathematics Competition)
Answer: $3<m<\frac{17}{3}$.