Although Jamie is ready to admit defeat and go home after the museum politely informed them that the clue they had found concerning the origin of the statue was not original, Claudia could not accept the fact that they had failed in their attempt to find Angel's creator. For her, proving that Michelangelo was in fact Angel's sculptor means more than just solving a mystery. Claudia feels a need to do something that will make her stand out, to let her be a heroine for just one moment. The realization that they have reached a dead end is devastating to her.
Just as they are about to buy their bus tickets home, Claudia remembers something that makes her feel they have one more chance to complete the task they have set for themselves. She recalls that Mrs. Basil E. Frankweiler, the former owner of Angel, lives in Farmington. Claudia has "a hunch" Mrs. Frankweiler will see them, and that she will know who the creator of the statue is. She begs Jamie to let her pursue this one last avenue in their search, and when she finally convinces him, he buys tickets for them to Farmington instead of to their home in Greenwich (Chapter 8).
Claudia and Jamie bought tickets to Farmington Conneticut because they wanted to get to California they closest way as possible