8.7. Squares in a grid that share a common edge are called adjacent. In a $7 \times 7$ grid, one Go stone is placed in one of the squares. It is allowed to place new stones in empty squares, but only in those that have at most one adjacent square occupied by a stone. How many stones can be placed in the grid at most?
8.7. Place chess pieces according to the rules while calculating the number of sides of the squares that have pieces (each side is counted only once, even if both squares on either side of the side have pieces. After placing the 1st piece, 4 sides are obtained, and each subsequent piece can add at most 3 new sides. Therefore, after placing the $n$-th piece, at most $3 n+1$ sides are obtained. Since there are a total of 112 sides in the grid, $3 n+1 \leqslant 112$. However, it is impossible to place pieces in all the edge squares of the grid, otherwise, when placing the last piece, its adjacent squares would already have pieces, so $3 n+1 \leqslant 111$. Thus, $n \leqslant 36$. An example of placing 36 pieces is shown in Figure 3.