Imagine an AI that can not only 'see' a 3D scene but also understand complex instructions like 'find the nightstand between the bed and desk, but not the one with a trash can beside it.' This level of 3D visual grounding (3DVG) is now within reach, thanks to a novel approach that frames the problem as a constraint satisfaction puzzle. Traditional 3DVG struggles with such nuanced queries. Existing AI models either rely on slow, laborious reasoning or make local interpretations that miss the big picture. The new Constraint Satisfaction Visual Grounding (CSVG) system changes the game. It uses an AI 'program generator' to create a virtual puzzle where objects are variables and their relationships are constraints. By solving this puzzle, the AI achieves a global understanding of the scene. This lets CSVG not only find the target object but also identify all related objects and handle negations ('not') and counting ('second,' 'third')—something current systems struggle with. Experiments on standard datasets like ScanRefer and Nr3D show CSVG’s superior performance, even outperforming some supervised methods that require extensive training. While CSVG currently focuses on spatial relations, future enhancements will incorporate object appearance (color, shape) and explore more dynamic constraint generation. This research opens exciting possibilities for robots navigating complex environments, augmented reality applications understanding our world, and many other real-world scenarios requiring precise 3D object identification.