The equations of motion for a golf ball interacting with a hole on a putting surface are found. A computer is used to predict the outcome of the ball’s encounter with the hole as a function of the impact parameter and the initial velocity of the ball at the rim. If the ball does not skid or bounce when it collides with the opposite rim, it is predicted that a uniform ball must travel at 1.626 m/s or less to be captured; that the British ball is easier to sink than the slightly larger American ball; that a ball with a larger moment of inertia is more difficult to sink; and that bouncing and skidding (factors that vary from green to green) result in capture at greater speeds. Experimental studies support these predictions.