The third question: In a $33 \times 33$ grid, each cell is colored with one of three colors, such that the number of cells of each color is equal. If two adjacent cells have different colors, their common edge is called a "separating edge." Find the minimum number of separating edges.

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Assume the number of separating edges is no more than 55, and denote the three colors as $A$, $B$, and $C$.

If a separating edge corresponds to two cells of colors $A$ and $B$ or $A$ and $C$, then it is called an $A$-colored separating edge. Similarly, define $B$-colored and $C$-colored separating edges.

Since $55 < 66$, there must be a column without horizontal separating edges or a row without vertical separating edges.
Assume there is a column without horizontal separating edges, and all cells in this column are $A$-colored.
(1) If the number of $A$-colored separating edges is no more than 32, then there must be a row without $A$-colored separating edges (otherwise, the number of $A$-colored separating edges would be at least 33, leading to a contradiction).
Thus, this row is a monochromatic row and is $A$-colored.
Therefore, the number of horizontal or vertical $A$-colored separating edges is no more than 16.

Assume the number of $A$-colored horizontal separating edges is no more than 16, then there must be 17 columns all $A$-colored, which contradicts the fact that the number of cells of each color is equal.
(2) If the number of $A$-colored separating edges is at least 33, then
(i) There exists a column entirely $B$-colored and a column entirely $C$-colored. Between these three columns, there are at least 33 vertical separating edges in each row (at least one in each row), hence there are at least 66 separating edges, leading to a contradiction.
(ii) There exists a column entirely $B$-colored, but no column entirely $C$-colored.
Since there is no row or column entirely $C$-colored, the number of $C$-colored separating edges
$\geqslant$ the length of the projection of all $C$-colored cells in the horizontal and vertical directions
$\geqslant 39$.
Otherwise,
the number of $C$-colored cells
$\leqslant$ the product of the lengths of the projections of all $C$-colored cells in the horizontal and vertical directions
$$
\leqslant 19 \times 19 < 363,
$$

leading to a contradiction.
If a $C$-colored cell is between a column entirely $A$-colored and a column entirely $B$-colored, then the horizontal projection of this $C$-colored cell is only one line segment. In this row, at least 2 $C$-colored separating edges are generated, so the contribution of this row to the difference between the left and right sides in conclusion (1) is 1. And between the $A$-colored column and the $B$-colored column, there is one vertical separating edge in each row. Suppose there are $k$ rows where there is a $C$-colored cell between the $A$-colored column and the $B$-colored column, then,
$$
\text{Number of } C \text{-colored cells} \geqslant 39 - k + 33 + k = 72,
$$

leading to a contradiction.
(iii) There is no column entirely $B$-colored, and no column entirely $C$-colored.

Similarly to (ii), the number of $B$-colored separating edges and $C$-colored separating edges is at least 39 each, and each separating edge is at least of two colors, hence

the total number of separating edges $\geqslant \frac{33 + 39 + 39}{2} = 55.5$, leading to a contradiction.
Construct an example with 56 separating edges, as shown in Figure 5.
Therefore, the minimum value is 56.