6. A $41 \times 41$ battlefield is divided into 1681 unit squares. A tank is hidden in one of these unit squares. A bomber aircraft bombs the battlefield. Each bombing targets one unit square. If the tank's square is not bombed, the tank remains in place; if it is bombed, the tank must move to an adjacent unit square (two squares are considered "adjacent" if they share a common edge). Destroying the tank requires hitting it twice. Throughout the process, the bomber pilot has no knowledge of the tank's location or whether it has been hit. Determine the minimum number of bombings required to ensure the tank is destroyed.
6. The minimum number of bombings is $\frac{3 \times 41^{2}-1}{2}=2521$.

Color all unit squares in a checkerboard pattern with black and white, and require that the squares at the four corners be black.

First, bomb all the white squares, then bomb all the black squares, and finally bomb all the white squares again. The number of bombings is
$41^{2}+\frac{41^{2}-1}{2}=\frac{3 \times 41^{2}-1}{2}=2521$.
If the initial tank is on a white square, it will be bombed in the first and second rounds; if it is on a black square, it will be bombed in the second and third rounds. In any case, it will be destroyed.

Next, we show that fewer bombings cannot guarantee the destruction of the tank.
First, each square must be bombed at least once.
Otherwise, a tank in an unbombed square will not be destroyed.

We then show that any two adjacent squares must be bombed at least three times in total.

Otherwise, suppose two adjacent squares $A$ and $B$ are each bombed once. Without loss of generality, assume $A$ is bombed first, followed by $B$. Then the tank in square $B$ will only be bombed once. Divide the battlefield, minus one black corner, into $\frac{42^{2}-1}{2}$ $1 \times 2$ or $2 \times 1$ "L" shapes.
Thus, the total number of bombings is no less than
$$
3 \times \frac{42^{2}-1}{2}+1=2521 \text {. }
$$