— Reaching is a critical task for humanoid robots, requiring the application of state-of-the-art algorithms for motion planning and inverse kinematics. Practical algorithms for solving these subproblems are currently not complete, offering resolution completeness or probabilistic completeness instead. While this lesser provision of completeness is acceptable in many cases, naively combining state-of-the-art approaches in motion planning and inverse kinematics can lead to a method that provides no measure of completeness. We present a resolution complete solution to the reaching problem for humanoid robots in static environments, and evaluate it against two other methods using a kinematically simulated humanoid in a virtual environment.