Act 4~ Hamlet

In Act 4 of Hamlet, we begin with the Queen, Gertrude telling King Claudius of Polonius' murder by Hamlet. She calls it an outrageous act and further reaffirms the idea that he has gone mad. In contrast, to Gertrude's reaction of disappointment and despair, Claudius is only relieved that the person dead was not him. In this one scene, we can see the contrast between Gertrude's real and raw emotions and Claudius' lack of empathy, sympathy, or any real emotion towards others. Yet when Hamlet is brought in to speak of the location of Polonius' dead body, Claudius becomes flustered and cannot seem to get his thoughts straight and organized. Hamlet's flippant responses show how he carefully and quickly outsmarted Claudius. 

QUESTION: How does Hamlet keep finding a way to outsmart Claudius?