I’m about 100 words, explain odysseus’s strategy to win back his home and his wife.

As much as he is eager to reclaim his property - home, land, and family - Odysseus mustn't rush, and he knows it all too well. His home is replete with suitors, waiting for Penelope to pick one out of them. She hesitates on purpose to buy some more time for her husband to return, but they take advantage of her hesitation to usurp Odysseus' property, eat his animals, abuse or seduce his female servants, disregarding the authority of the absent master of the house. So, Odysseus can't just attack them and risk defeat, which would mean catastrophe for his family. Besides pure caution he feels as a military man, he has another aim: to put all of his household (including his wife) to test. Have they been loyal to him all this time? Have they forgotten him? He prepares for a bloody feast. He is about to murder people. Naturally, he wants to make sure who deserves what.

So, with Athena's help, Odysseus disguises as a beggar. He decides to test all the people's hospitality toward the lowest of the low. Of course, the suitors treat him badly, whereas some of the servants are compassionate and respectful toward the unknown old man in tatters. So, there's the first demarcation line that separates people who are going to live from those who are deserving to die. His old nursemaid recognizes him by a scar while washing his feet - so, he hasn't been forgotten. The last test is for Penelope herself: has she forgotten their bed, as a metonymy of their marriage? When she proves she hasn't, he has all the proof he needed. His wife hasn't forgotten him, in spite of all the years and temptations. So, his vengeance and punishment of the suitors have not been in vain.