# Minimum Number Of Rooks

Find the smallest positive integer $$k$$ for which the following statement is true.

Suppose $$k$$ rooks are placed on a $$2014 \times 2014$$ chessboard. Then, there must exist three rooks, call them $$r_1, r_2, r_3,$$ such that $$r_1$$ attacks $$r_2,$$ $$r_3$$ also attacks $$r_2$$, but $$r_1$$ doesn't attack $$r_3$$.

Details and assumptions

• Two rooks are said to attack each other if they lie on the same row or same column.
• The $$k$$ rooks are placed on distinct cells, i.e. a cell contains at most one rook.
• The given condition must hold for any configuration of $$k$$ rooks.
• This problem is not original.
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