11. If in a $4 \times 4$ grid of 16 cells, each cell is filled with a number such that the sum of the numbers in all adjacent cells of each cell is 1, then the sum of the 16 numbers in the grid is $\qquad$
(Note: Adjacent cells refer to cells that share exactly one edge)
11.6.

First, fill the 16 squares with the English letters $A, B, C$, $\cdots, O, P$ (as shown in Figure 8). Given that for each square, the sum of the numbers in all adjacent squares is 1, so,
$$
\begin{aligned}
16= & 2(A+D+M+P)+3(B+C+E+H+ \\
& I+L+N+O)+4(F+G+J+K) \\
= & 2(A+B+C+\cdots+O+P)+(B+C+E+ \\
& H+I+L+N+O)+2(F+G+J+K) \\
= & 2(A+B+C+\cdots+O+P)+(B+E+J+
\end{aligned}
$$
$$
\begin{array}{l}
G)+(C+F+K+H)+(F+I+N+K)+ \\
(G+J+O+L) .
\end{array}
$$
$$
\begin{array}{l}
\text { and } B+E+J+G=C+F+K+H \\
=F+I+N+K=G+J+O+L=1,
\end{array}
$$

Therefore, 16 $=2(A+B+C+\cdots+O+P)+4$. Hence, the sum of the 16 numbers in the grid is
$$
A+B+C+\cdots+O+P=6
$$