In Hamlet, what information about the death of Polonius does Hamlet keep from Claudius?

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The answer to this question can be found in Act IV scene 3. This comes after Act IV scene 2, where Rosencrantz and Guildenstern try and find out where Hamlet has stowed the body of Polonius. There inability to find out the truth causes Polonius to try and get the location of the corpse out of Hamlet himself, and he finally manages to get this information after repeatedly asking Hamlet and receiving answers that play on words and deliberately frustrate him until finally Hamlet reveals the truth:

But indeed, if you find him not this month, you shall nose him as you go up the stairs into the lobby.

Hamlet's deliberate concealing of the location of the body of Polonius at this stage in the play seems more calculated to annoy and frustrate rather than anything else, as suggested by the delight with which Hamlet puns in his responses to Claudius before revealing the truth. The insistence with which he refuses to give a clear answer and conceals the truth strongly suggests that he is enjoying the discomfort that this causes the king, especially because, in one sense, Claudius has managed to escape being killed, as originally, Hamlet thought that it was Claudius concealed behind the arras rather than Polonius.

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