and at the beginning tells various lies to them and acts in a ridiculous way. However, the conflict of this novel is her own internal conflict to accept the fact that she is not going to be rescued by her mother and that she can be herself and learn to love and be loved by those around her. The resolution of this conflict is indicated when she finally receives an invitation from her mother at the end of the novel to go to Palm Springs and spend some time with her. April's response makes it clear that she has come to love her Grandma and her new friends in the Egypt Club and that she is happy with herself and her lot in life:

But Grandma and I have our plans all made for Christmas Eve and I have a date to spend part of Christmas Day with my friend, Melanie. So I guess I can't make it this time.

This story therefore tells the gradual, moving story of one girl's journey to accept both herself and her position in life. This is the central conflict that dominates the narrative. Finally, at the end of the story, she has found a place to belong and her own identity that involves acceptance of who she is rather than who she feels she needs to be in order to be loved and to be accepted.

I believe that there are two main conflicts going on in The Egypt Game. One conflict is an external conflict that affects the children as well as the greater community at large. That conflict is focused on the murderer that is somewhere present within the neighborhood. This conflict comes to a climax when April and Marshal are attacked by this person. The attack is thwarted by the Professor, who happens to be nearby and sees the attack. He calls for help, and the kids are able to get away. The murderer is caught soon after, and the neighborhood is returned to safety.

The other main conflict is an internal conflict for April. April has been forced to move into the neighborhood, and she isn't sure if she wants to stay there living with her grandmother. This conflict is also resolved by the end of the book. April has made several good friends, and she has discovered that she is happy with the place and the friendships that she has made.

I think you are refering to the second chapter of this excellent book, because the book actually starts in media res, or in the middle of things, and then cuts to the beginning in the second chapter. This chapter introduces a very important character and her central conflict. April Hall has been sent to live with her grandmother by her mother, however April deeply resents this and feels that this is just a temporary arrangement, and that her mother will send for her very soon. Note how this second chapter introduces the scenario:

Exactly one month before the Egypt Game began in the Professor's backyard she had come, very reluctantly, to live in teh shabby splendour of an old California-Spanish apartment house called the Casa Rosada. She came because she had been sent away by Dorothea, her beautiful and glamorous mother, to live with a grandmother she hardly knew, and who wore her grey hair in a bun on the back of her head.

April's conflict thus lies in the way that she has been effectively sent away by her mother to live with a stranger. She refuses to settle down in this place, as this would signal that she recognises her mother is highly unlikely to send for her and ask her to come and live with her again.