1. **Problem statement:** Place 3 rooks on a chessboard so that two rooks attack each other vertically (up and down) and two rooks attack each other horizontally (left and right). 2. **Important rules:** - Rooks attack along rows and columns. - Two rooks attack each other vertically if they share the same column. - Two rooks attack each other horizontally if they share the same row. 3. **Goal:** Find positions for 3 rooks such that: - There is a pair of rooks in the same column (vertical attack). - There is a pair of rooks in the same row (horizontal attack). 4. **Step-by-step reasoning:** - Let the rooks be at positions $(r_1,c_1)$, $(r_2,c_2)$, and $(r_3,c_3)$ where $r_i$ is the row and $c_i$ is the column. - For vertical attack: two rooks share the same column, so $c_i = c_j$ for some $i \neq j$. - For horizontal attack: two rooks share the same row, so $r_k = r_l$ for some $k \neq l$. 5. **Example placement:** - Place rook 1 at $(1,1)$. - Place rook 2 at $(2,1)$ to have vertical attack with rook 1 (same column 1). - Place rook 3 at $(1,2)$ to have horizontal attack with rook 1 (same row 1). 6. **Verification:** - Rook 1 and rook 2 share column 1 (vertical attack). - Rook 1 and rook 3 share row 1 (horizontal attack). - Rook 2 and rook 3 do not attack each other. 7. **Final answer:** - Place rooks at positions $(1,1)$, $(2,1)$, and $(1,2)$. This satisfies the problem conditions.