\(\ 1\).(\(\ 16\) marks)Consider a chessboard of size \(\ 8\) units\(\ \times8\) units (i.e., each small square on the board has a side length of \(\ 1\) unit).Let \(\ S\) be the set of all the \(\ 81\) vertices of all the squares on the board.What is the number of...