Methods for determining the intercalary month in a Chinese calendar-making system: a problem of probability (Q2719693)

There are principally three methods for intercalating the leap month in the history of Chinese calendar-making system: the earliest one can be found in the \textit{Sanlitong} from 104 BC, the next one is described in the later Han dynasty calendar \textit{Sifenli} (85 AD) and much later a method in the famous \textit{Dayan} calendar from 724 AD. Since no single algorithm can determine a leap month completely, those methods created by calendar-makers can only predict a possible position of a leap month. In this article, Qu Anjing discusses how many possible results of a leap month could occur with respect to the one predicted by the calendar system. The author also deduces their respective probability formulae.