In which book of The Odyssey does Penelope outsmart the suitors?
Penelope of course engages in many ways to trick the suitors and prevent her having to decide to marry them, but one specific incident where she clearly tricks them into giving her gifts and wealth is in Book 18, when she is clothed in beauty thanks to the goddess Athena and uses that beauty to encourage the suitors to give her gifts that are fitting with their role as suitors. Note what she says to Eurymachus and how she persuades the suitors to be generous with their belongings:
But herein has bitter grief come upon my heart and soul, for such as yours was never the way of wooers heretofore. They who are fain to woo a lady of worth and the daughter of a rich man and vie with one another, these bring of themselves cattle and goodly flocks, a banquet for the friends of the bride, and give to her glorious gifts; but they do not devour the livelihood of another without atonement.
Penelope is therefore shown to use her cunning and her natural beauty in order to challenge them and also to take from them freely gifts and wealth that only enriches her own position. Her speech both mocks the suitors and also forces them to show their intentions towards her through the gifts that they bring her. This is something, incidentally, that Odysseus witnesses and admires. Penelope therefore outsmarts those suitors in the same way that the wily Odysseus outsmarts so many other characters in this text, showing that they are well suited for each other.