What is the size of the tank? $1 \times 1$ ? Also, is the answer $51$? @2below Is time a constraint?

Is their some condition like the tank cannot trace a cell twice?

Isn't the answer 1? Assume that the cannon takes 5 minutes to fire at any one cell. Then it takes 10 minutes for the tank to move to an adjacent square. You are firing at 96 squares per day. Theoretically, the cannon should hit the tank after some time. I'm probably wrong though.

i have got a upper bound of 15 so far by construction. And it's definitely not 1(any box has atleast 2 ways out)

Dem0nfang wrote: What is the size of the tank? $1 \times 1$ ? Obviously. Quote: @2below Is time a constraint? Not at all. The tank moves immediately after a shot. A-Thought-Of-God wrote: Is their some condition like the tank cannot trace a cell twice? No.

This problem appears as theorem 3 in the following paper: http://www.math.bas.bg/moiuser/~ACCT2016/a7.pdf

After a tank shoots at $k$ spots, will it never shoot those $k$ spots again? Also, does the tank start anywhere? Or at the first cell?

The problem is Intersting....... Bummp

One can use St Petersburg MO 2017 9.7. Just see on every turn how many possible cells are there for the tank before it moved (this works even if we suppose we know the color of the cell of the tank in the beginning (supposing we have a checkerboard coloring)). This is for the proof that $k=50$ does not work.

can anyone provide construction for k=51?