What does Digory decide he must do to get rid of the Witch in The Magician's Nephew?
In order to get rid of the Witch, whom he has inadvertently brought into our world, Digory decides that he must try to get her back into the Wood between the Worlds, where she seemed to become weak and "all faint." In order to do this, Digory must arrange things so that he can slip on his yellow ring while touching her, then they both will be transported to that mysterious, in-between place.
When Digory and Polly had been acosted by the Witch in her own land, they had tried to escape her by touching their rings, which had the power to transport them home. Unfortunately, the first time they had tried to get away, the Witch had been "holding fast to Polly's hair," and so had been taken with them. Instead of getting back home directly, however, the children and the Witch had found themselves in the mysterious wood, where, inexplicably, the Witch had become pale, and had seemed to be losing her power. Attempting to escape once again, Digory and Polly had leaped into the pool they recognized as leading home, but again, the Witch had managed to tag along, this time gripping Digory by the ear as he disappeared into the water. The children and the Witch emerged in the midst of the children's home in our world, London, where the Witch went off to generally wreak havoc. Knowing that he must get the evil woman away from our world, Digory plots to take her back to the Woods in-between, where he hopes her powers will be rendered insignificant.