1. In a $4 \times 4$ grid, eighteen lines can be drawn, including eight lines (four horizontal and four vertical), and five diagonal lines from the top left to the bottom right and from the top right to the bottom left. These diagonal lines may pass through 2, 3, or 4 small squares. Ten chips are to be placed in the grid, with a maximum of one chip per small square. If a line has an even number of chips, 1 point is scored. What is the maximum number of points that can be scored?
2. As shown in Figure 11, the maximum score is 17.
The following proves that 18 points cannot be achieved.
Notice that, in Figure 11, there are always two opposite corner cells not covered by the same direction of five diagonal lines, and these two cells must be either both empty or both full. At the same time, there must be one row and one column that are full. Consider three scenarios.
(1) All four corner cells are empty.
By symmetry, assume without loss of generality that the second row and the second column are full. In this case, another cell in the first row, fourth row, first column, and fourth column must be filled. This requires at least 11 chips in total.
(2) Exactly two diagonal cells are empty.
By symmetry, assume without loss of generality that one of the cells is in the first row and first column, and the other is in the fourth row and fourth column. Then, one chip must be placed in the first row, first column, fourth row, and fourth column. This indicates that the four internal cells must all contain chips.

By symmetry, assume without loss of generality that the full row is the second row. In this case, the length-2 diagonals intersecting the second row cannot all score.
(3) All four corner cells are full.
Claim: The full row is either the first row or the fourth row.
If the second row is full, then the first column and the fourth column must also be filled, which already uses 10 chips, but multiple diagonals cannot score. This confirms the claim.

By symmetry, assume without loss of generality that the first row and the first column are full. In this case, no matter how the remaining 2 chips are placed, some diagonal will not score.