Consider any sequence of less then $$$n + \left[\frac{n}{2}\right]$$$ moves. Then there will be more then $$$\left\lceil\frac{n}{2}\right\rceil$$$ cells that are used no more than 1 time (Dirichlet principle). This means that there will be a pair of consecutive cells that are used no more than 1 time. Now consider a tank in the cell which is being bombed later. If this tank moves to the other cell, it wont be hit for the second time.