Find the smallest positive integer for which the following statement is true.
Suppose rooks are placed on a chessboard. Then, there must exist three rooks, call them such that attacks also attacks , but doesn't attack .
Details and assumptions
- Two rooks are said to attack each other if they lie on the same row or same column.
- The rooks are placed on distinct cells, i.e. a cell contains at most one rook.
- The given condition must hold for any configuration of rooks.
- This problem is not original.