The solution is 2521 Explanation:
Suppose you checker the 41x41 field such that there are two colors, white and black, and no adjacent squares have the same color. Therefore 840 squares are black and 841 are white, or vice-versa. Suppose the tank is in a black square. If you hit all black squares, the tank will move to a white square, because there are no adjacent black squares. Therefore you can bomb all the white squares and the tank is killed. So, to definitely kill the tank, your run must include one bombing of all black squares followed by one bombing of all white squares. The situation is similar if you start with white. So, your run must include one bombing of all white squares followed by one bombing of all black squares. The shortest run that satisfies all these requirements is black-white-black, which requires 840+841+840=2521 bombs to be dropped.