What do mahjong tiles and menopause have in common?
Solution 1:
I actually agree with RegDwigнt that this looks like sloppy writing. The cause of the confusion looks to be that this line is very thinly related to the episode title (and probably theme of the episode).
In The Analects of Confucius, there is a section named "Words and Deeds," and is no doubt where the episode title came from. The show, House, is known for extremely subtle and/or obscure jokes and references. I would assume that if you rewatched the episode, there would be more references to Confucius as well.
Wikipedia description (emphasis mine):
The importance of education and study is a fundamental theme of the Analects. For Confucius, a good student respects and learns from the words and deeds of his teacher, and a good teacher is someone older who is familiar with the ways of the past and the practices of antiquity (Analects 7.22).
The link here is that there is some people believe that Confucius invented Mahjong.
One of the myths of the origin of mahjong suggests that Confucius,1 the Chinese philosopher, developed the game in about 500 BC. The three dragon (cardinal) tiles also agree with the three cardinal virtues bequeathed by Confucius. Hóng Zhōng (紅中 , red middle), Fā Cái (發財 , prosperity), and Bái Bǎn" (白板 , white board) represent benevolence, sincerity, and filial piety, respectively.
The myth also claims that Confucius was fond of birds, which would explain the name "mahjong" (maque 麻雀 = sparrow).
Usually, the menopause joke would probably have been about playing Bridge or Canasta, but the writers decided to tie this line to the episode theme by using Mahjong instead. However, because the reference is so obscure, and Mahjong does not fit in our Western stereotypes of post-menopausal women, the joke falls flat and becomes confusing.