# The Minimum Number Of Kings

Discrete Mathematics Level 5

A certain number of kings are placed on a $$2014 \times 2014$$ chessboard. A cell on a chessboard is called occupied if a king is placed on it. A cell is called vulnerable if it shares an edge with an occupied cell. Let $$N$$ be the minimum number of kings that must be placed on the chessboard to make sure all cells in the chessboard are vulnerable. Find the last three digits of $$N.$$

Details and assumptions

• In other words, there should exist no configuration with smaller than $$N$$ kings which makes all cells vulnerable. But, $$N$$ kings can be placed in such a way that all cells are vulnerable.
• A cell that is occupied need not be vulnerable.
• This problem is not original.
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