I appreciate the response! For the $3$ queens problem, how many different arrangements of $3$ queens $($Q$\_1,$ Q$\_2.,$ Q$\_3)$ are possible in a $3\backslash$times $3$ chessboard under the following conditions: $-$ Queens in the same rows, columns or diagonals as other queens are considered under attack. The arrangements you are counting should be such that no queens should be under attack. $-$ Q$\_1$ should be in row $1,$ Q$\_2$ should be in row $2,$ Q$\_3$ should be in row $3.$ Derive the arrangement$/$s by drawing a state space tree and illustrating backtracking. Finally list out the arrangements. Note: The graph $($tree$)$ that you see in n$-$Queens problem Backtracking: Recording is called the state space tree.