Penelope keeps the suitors at bay for how many years with her weaving scheme.

The answer is indeed three years.

Explanation:

Penelope wants to remain faithful to her husband Odysseus, even though he's been gone for a long time and people believe him to be dead. She lies to the men who wish to marry her by telling them she will choose and marry someone when she finishes weaving a burial shroud for Laertes, Odysseus' father.

The weaving is never done, since Penelope keeps undoing her own work. By the fourth year of doing so, her maids tell her suitors the truth. They - the suitors - demand that she finish it, and so she does.

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