N queen puzzle is the problem of placing n chess queens on nxn dimensional chessboard such that the solution exists when none of the queens share any column, rows or diagonally intersect each other in the chessboard.
Hill climbing is a Local search technique which finds the optimal solution iteratively by incrementing the improvements after each iteration starting from an arbitrary solution.
To avoid getting stuck at local maxima as the solution one could use many variations with Hill Climbing such as repeated local search (random restarts), iterated local search, or memoryless stochastic modifications usually known as simulated annealing.