2. On a plane, there is an $8 \times 8$ grid colored in a black and white checkerboard pattern. Basil arbitrarily selects one of the cells. Each turn, Peter draws a polygon (which can be concave but not self-intersecting) on the grid, and Basil will honestly inform Peter whether the selected cell is inside or outside the polygon. To ensure that he can determine whether the cell Basil chose is white or black, what is the minimum number of turns Peter needs to ask?
2. If the polygon drawn by Peter includes only all the cells of a certain color, then this polygon must intersect itself. Therefore, Peter cannot determine the color of the cell chosen by Basil in just one round.

Next, two strategies are given that can determine the color of the selected cell in two rounds.

【Strategy 1】The two polygon drawing methods shown in Figure 1 can determine whether the selected cell is white or black in two rounds.

If the selected cell is white, the answers in both rounds will either be inside the drawn polygon or outside the drawn polygon. If the selected cell is black, then in these two rounds, it will appear once inside the polygon and once outside the polygon.

【Strategy 2】The two polygon drawing methods shown in Figure 2 can also determine the color of the selected cell in two rounds. In the first round, draw the polygon in Figure 2 (a). If the selected cell is outside the polygon, it must be in the 2nd, 4th, 6th, or 8th column from left to right. In the second round, draw the polygon in Figure 2 (b), and determine whether the selected cell is black or white based on whether it is inside or outside the polygon. If the answer in the first round is inside the polygon, then the cell must be in the 1st, 3rd, 5th, or 7th column from left to right, or in the last row from top to bottom. In the second round, use the polygon in Figure 2 (c).

If the answer is inside the polygon, the selected cell is white; if the answer is outside the polygon, the selected cell is black.

【Note】If the problem does not require drawing the polygon within the table (i.e., it can be understood as being able to draw outside the table), then Strategy 1 can be simplified as shown in Figure 3.