Predicting religious holidays

Ever wondered why it's so difficult to portend when Hari Raya Puasa/Haji, Deepavali, Vesak Day, Chinese New Year comes every year? Fret no more, as an NUS Maths professor explains how the different calendars (lunar, solar, Gregorian, lunisolar etc.) come together to make planning leave so chaotic.

Source: http://www.math.nus.edu.sg/aslaksen/calendar/public-talk.pdf