Seven paintings currently attributed to Johannes Vermeer and one related work do not fit in with his distinctive approach, level of skill, use of materials, or gradual development, yet were based on the same interiors, furniture, objects, and family members as models. Several of these compositions also copy, adapt, and combine elements from his paintings. Vermeer did not have any official students, but he was not required to register his own children as students. Here I argue that his eldest daughter Maria Vermeer became his apprentice around 1672 at roughly the age of eighteen. Maria's features as model for her father's paintings are also recognizable in her earliest self-portrait studies. Over the next three years, she based her compositions on Vermeer's paintings, using herself and other family members as models. The eight paintings examined here share mutual idiosyncrasies, strategies, and a palpable development. They were created in a complex artistic dialogue with Vermeer, and ultimately influenced him in turn. My account is based primarily on the visual evidence of the paintings, starting with a coherent chronology of Vermeer's works, which can be related in turn to the chronology of Maria Vermeer's paintings from her brief period as his apprentice. Another dimension involves the family members they portrayed, primarily Vermeer's second eldest daughter Elisabeth. A last crucial factor are written documents: an agreement between the painter's widow and a baker to pay a large debt for bread, and the 1696 auction of Vermeer paintings that were originally owned by Vermeer's patron. All these elements are inter-related in a complex puzzle that is inextricable from the riddle of the Sphinx of Delft — his unique approach, vision, and genius.