The Mah Rabu Guide to Single and Double Torah Portions
The basic idea: The Torah is divided into 54 portions. The last one (Vezot Haberachah) is only read on Simchat Torah when completing the Torah, and is never read on a regular Shabbat. So call it 53 that have to be distributed across the regular Shabbatot of the year. A non-leap year has 353-355 days (50-51 weeks), and a leap year has 383-385 days (54-55 weeks). But the regular Shabbat reading is never read if the Shabbat happens to be a holiday. It differs from year to year whether a given holiday falls on Shabbat, but there is always at least one Shabbat during Sukkot and one during Pesach. This means that the total number of non-holiday Shabbatot in a given year can range from 46 to 53. To address this, anywhere from 0 to 7 sets of Torah portions are doubled up.
So the general principle behind these rules is that any time an extra (non-holiday) Shabbat is added, a pair of Torah portions is read individually, and any time a Shabbat is removed, a pair of Torah portions is read together.
- Acharei Mot-Kedoshim
Exceptions: In a non-leap year that begins on Thursday, an extra Shabbat is squeezed in, because Simchat Torah at the beginning of the year is on Thursday (or Friday), right before Shabbat. There are two such types of years. In a 355-day year beginning on Thursday (i.e. the following year begins on Tuesday), Vayakhel and Pekudei are read separately to cover the extra Shabbat. In a 354-day year beginning on Thursday (i.e. the following year begins on Monday), communities that observe 2 days of yom tov don't need to worry (and all 4 of these pairs are read as double portions) because the 8th day of Pesach takes up one Shabbat. However, in this type of year, communities that observe 1 day of yom tov read Behar and Bechukotai separately. This means that 1-day and 2-day communities are reading different Torah portions for several weeks after Pesach.
Exception 1: In a leap year beginning on a Thursday, Matot and Mas'ei are read separately, for the same reason discussed above (there is an extra Shabbat in the year).
Exception 2: In a leap year in which the following year begins on a Monday, there is also an extra Shabbat at the end of the year. In 2-day yom tov communities, this extra Shabbat is absorbed by the 8th day of Pesach (as above), so Matot-Mas'ei is combined as usual. However, in 1-day yom tov communities, Matot and Mas'ei are read separately. In these rare cases (covering about 10% of all years), the 1-day and 2-day calendars disagree for about 3 months (rather than just for a few weeks, which happens in 29% of years due to Shavuot and 18% of years due to Pesach).
Now here's the shorter version which may be easier to remember, and covers most cases:
- Vayakhel-Pekudei / Tazria-Metzora / Acharei Mot-Kedoshim / Behar-Bechukotai: always separate in leap years; usually combined in non-leap years
- Chukat-Balak: combined if the 2nd day of Shavuot is on Shabbat
- Matot-Mas'ei: usually combined
- Nitzavim-Vayeilech: combined if Rosh Hashanah or Yom Kippur is on Shabbat