Yahoo Chiebukuro... was it? That's where I looked it up!
Yahoo Chiebukuro: think Yahoo Answers, only it's in Japanese, still active, and actually useful a lot of the time.
The 29th of January is
The Anniversary of the Census!
Census → 人口調査
Investigation → 調査
That's why she's in a Sherlock-esque attire
On this day, back in 1872, the first Japanese country-wide family register survey was implemented!
By the way, according to my research, the population of Gensoukyou is said to amount to 1000 to 2000 inhabitants at most!