Question 3
The set $G$ is defined by the points $(x, y)$ with integer coordinates, $1 \leq x \leq 5$ and $1 \leq y \leq 5$. Determine the number of five-point sequences $\left(P_{1}, P_{2}, P_{3}, P_{4}, P_{5}\right)$ such that for $1 \leq i \leq 5, P_{i}=\left(x_{i}, i\right)$ is in $G$ and $\left|x_{1}-x_{2}\right|= \left|x_{2}-x_{3}\right|=\left|x_{3}-x_{4}\right|=\left|x_{4}-x_{5}\right|=1$.