What personal qualities do Sayuri and Mameha have that make them able to survive and prosper in Memoirs of a Geisha?
Both Mameha and Sayuri are intelligent and kind, and these qualities help them survive and prosper in spite of the many cruelties they must suffer. Mameha is not the most beautiful geisha; Hatsumomo, her rival, is much more gifted in this area. Yet Mameha is one of the most successful geishas in Japan, and she is able to get by during hard times while Hatsumomo is not. Mameha has a deep understanding of social politics in the city of Gion, and is at heart a good and sensible human being. She acts with thoughtful dignity at all times and is loved because of her kindness and sensitivity towards others, in contrast to Hatsumomo, who reigns with haughty pride and cruelty.
Sayuri is lovely, known for her unusual light-colored eyes. Like Mameha, she is a decent woman, and does not use her beauty to satisfy her selfish pride. She is intelligent and clever, quickly picking up the things she must learn in order to survive as a geisha, and she is resilient, able to endure the disappointments and cruelties visited upon her by the vagaries of the social system and by Hatsumomo in particular. Despite her profession, Sayuri has a truly imaginative and romantic nature. She carries from childhood the dream of being adopted by the Chairman, recognizing his benevolence and honorable character; the Chairman is her inspiration as Sayuri struggles to become a great geisha. Sayuri's whole life is driven by her longing to be with the Chairman. She astutely and regretfully manipulates the system to thwart the intentions of another suitor, Nobu, and in the end is rewarded for her single-minded fidelity when the Chairman becomes her danna, or sponsor, until his death. Sayuri has a sensitive and introspective nature, and retains her sense of humanity throughout her life, despite all she has had to endure.
Tanaka-san never became her danna, it was the Chairman who did until his death later on in the story. She was driven to be with the Chairman since he helped her when she was unhappy on the bridge.. I think it was the bridge. From "that brief encounter with the Chairman" she "had changed from a lost girl facing a lifetime of emptiness to a girl with the purpose in her life."(133 Ch. 9)