1. **Stating the problem:** We are given a sequence of figures where the number of squares in each figure follows a pattern. The table shows figure number $x$ and number of squares $y$ as: 1 | 1, 2 | 4, 3 | 9, 4 | 16. 2. **Observing the pattern:** Notice that $y$ values are perfect squares: $1=1^2$, $4=2^2$, $9=3^2$, $16=4^2$. The second difference is constant and equals 2, which is characteristic of quadratic sequences. 3. **Formula for the number of squares:** The formula relating figure number $N$ to the number of squares $y$ is: $$y = N^2$$ This means the number of squares in Figure $N$ is the square of $N$. 4. **Explanation:** Each figure adds a layer of squares forming a perfect square shape. For example, Figure 1 has $1^2=1$ square, Figure 2 has $2^2=4$ squares arranged in a $2 \times 2$ block, and so on. 5. **Summary:** The pattern is quadratic, and the formula $y = N^2$ perfectly describes the number of squares in Figure $N$.