We fill a 3 \times 3 grid with 0s and 1s. We score one point for each row, column, and diagonal whose sum is odd.
\begin{array}{|c|c|c| }
\hline
1 & 1 & 0 \\
\hline
1 & 0 & 1 \\
\hline
0 & 1 & 1 \\
\hline
\end{array}
\hspace{1cm}
\begin{array}{|c|c|c|}
\hline
1 & 1 & 1 \\
\hline
1 & 0 & 1 \\
\hline
0 & 1 & 1 \\
\hline
\end{array}
For example, the grid on the left has 0 points and the grid on the right has 3 points.
(a) Fill in the following grid so that the grid has exactly 1 point. No additional work is required. Many answers are possible. You only need to provide one.
\begin{array}{|c|c|c|}
\hline
\; & \; & \; \\
\hline
\; & \; & \; \\
\hline
\; & \; & \; \\
\hline
\end{array}
(b) Determine all grids with exactly 8 points.
(c) Let E be the number of grids with an even number of points, and O be the number of grids with an odd number of points. Prove that E=O.