7. In a $10 \times 10$ grid, there is a shape composed of $4 n$ $1 \times 1$ small squares, which can be covered by $n$ "田" shaped figures, or by $n$ "世" or "円" shaped figures (which can be rotated). Find the minimum value of the positive integer $n$.
(Zhu Huaiwei, problem contributor)
7. Let the given shapes be denoted as type $A$ and type $B$.

First, we prove that $n$ is even.
Color the $10 \times 10$ grid as shown in Figure 6.

Regardless of which 4 squares type $A$ covers, the number of black squares must be even, while for type $B$ it is odd. If $n$ is odd, the number of black squares covered by $n$ type $A$ shapes must be even; while the number of black squares covered by $n$ type $B$ shapes must be odd, leading to a contradiction. Therefore, $n$ must be even.

If $n=2$, the shapes formed by two type $A$ shapes can only be the two cases shown in Figure 7. However, neither of these can be formed by two type $B$ shapes.
Thus, $n \geq 4$.
Figure 8 shows the tiling when $n=4$.