14. (15 points) Divide a large square with a side length of 7 into smaller squares with side lengths of 1, 2, or 3. What is the minimum number of squares with a side length of 1? Draw your division method in the diagram. Answer: There are at least $\qquad$ squares with a side length of 1.
【Solution】Solution: Let the number of $3 \times 3$ squares be $x$, the number of $2 \times 2$ squares be $y$, and the number of $1 \times 1$ squares be $z$. Then we have the equation: $9 x+4 y=49-z$. Simple trials show that $x \leqslant 4, y \leqslant 9$. When $z=0$, solving $9 x+4 y=49$ gives $x=5, y=1$ (discard); $x=1, y=10$ (discard). When $z=1$, solving $9 x+4 y=48$ gives $x=4, y=3$ (discard); $x=1, y=12$ (discard). When $z=2$, solving $9 x+4 y=47$ gives $x=3, y=5$ (discard, as it is found that if 3 $3 \times 3$ squares are used, it is impossible to place 5 $2 \times 2$ squares). When $z=3$, solving $9 x+4 y=46$ gives $x=2, y=7$. Trying to draw it, it is found that the condition can be satisfied. As shown in the figure below: Therefore, the answer is: 3.