Question 87
A necromancer and a paladin combat on a $666 \times 666$ grid. The grid is initially empty. For each turn, the necromancer first chooses a block on the grid, and increases one skeleton in each block within the $3 \times 3$ region centered at the chosen block (which include at most nine blocks); then, the paladin chooses four blocks on the grid, and eliminates one skeleton from each of these blocks (the number of skeletons in each block is a non-negative integer.)
For any turn, we called a block **doomed** if, at the end of that turn, there are $10^6$ or more skeletons in that block. Find the largest positive integer $K$ such that the necromancer has a strategy that guarantees $K$ or more blocks on the grid to be simultaneously doomed in some finite turns, regardless of how the paladin acts.
For any turn, we called a block **doomed** if, at the end of that turn, there are $10^6$ or more skeletons in that block. Find the largest positive integer $K$ such that the necromancer has a strategy that guarantees $K$ or more blocks on the grid to be simultaneously doomed in some finite turns, regardless of how the paladin acts.