Packing problems are a classical topic in combinatorics and theoretical computer science with many practical applications. The goal of these problems is to arrange a set of objects within a bounded space under certain constraints, commonly optimizing a metric, such as maximizing the number of objects placed. This thesis explores a geometric packing problem on a two-dimensional grid, where non- overlapping, axis-aligned squares must be placed such that each square "sees" exactly K other squares along horizontal or vertical lines. To find configurations that maximize the number of placed squares, we adapt the classical backtracking framework and introduce two algorithmic methods for exact searches. Additionally, we implement a simulated annealing approach to produce approximate solutions, thereby reducing search times for larger grid sizes where exhaustive search becomes computationally infeasible. We also discuss how problem-specific properties, such as symmetry of solution grids, can accelerate searches and find lower bounds on the maximal number of placable squares.