Most people are aware of the first rule for calculating the day of the week for rosh hashana, לא אד"ו ראש , Rosh hashana can not come out on a sunday, wed or fri. This happens about 7 times in a cycle of 19 years. There are three other rules. The last rule occurs only every two hundred years or so. This is it.

Shana tova

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Rosh hashana can not come out on a sunday, wed or fri. This happens about 7 times in a cycle of 19 years.

What happens about 7 times in a cycle?

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There are three other rules. The last rule occurs only every two hundred years or so. This is it.

What are the 3 other rules? What is the last rule?

Here's the answer from last week's Torah Tidbits published by the OU Center in Yerushalayim:

In our fixed calendar, Rosh HaShana is fixed on a particular day, based on the molad of Tishrei and four rules of postponement. RH begins on the day of the molad of Tishrei, unless... [1] if the molad is after noon, then RH is set for the following day. [2] If the day is SUN, WED, or FRI, then RH is the following day. Either [1] or [2] can postpone RH by a day (from the day of the molad), or they can both cause a 2-day postponement. RH is the day of the molad less than 25% of the time. [1] and/or [2] account for over 70% of the postponements of RH. 2 other rules: 1 occurs 3.3% of the time and the fourth rule, the one that fixes RH this coming year on TUE occurs a bit more than ½%.

The 4th D'chiya (postponement of RH from the day of the molad) rule: In a year following a 13-month year), if the molad of Tishrei is Monday morning after 9h 32m 13p, even if it is before noon, RH is set on Tuesday. Last occurrences: 5688, 5519, 5441, 5194.

If RH would stay on MON, the day of the molad of Tishrei, the previous year, 5765 would have only 382 days, which cannot be. By moving to TUE, it gives 5765 its 383 days.

Well if you could understand that description, you wouldn't need to ask. These calculations are way beyond the information the average jew or even yeshiva graduate understands. The Sun., Mon. Fri rule is easy to understand in part, as most people can understand why it would be inconvenient to have yom kippur the day before or after Shabbat, especially in times when one bought their food fresh everyday.

The Sun., Mon., Fri. rule (rosh hashana can not be on these days of the week), bring me to one of my riddles.

Why are there four possible shabbatot in a year that we take out three sefer torahs in Israel, but only three in the Golah (outside of Israel).

Four possibles
Shabat Chanuka Rosh Chodesh
Shabat Shekalim Rosh Chodesh
Shabat Chodesh Rosh Codesh
Simchat Torah
Simchat Torah is one day in Israel so it might come out on Shabbat. Outside of Israel, Simchat Torah comes is the on the second day of Shemini Atzeret and the second day can never be on Shabbat due to the Sun, Wed, Fri rule.

When I was growing up, I assumed that they would take out four torahs on Simchat Torah in Israel, one for the parshah, one for the reading for the day, one for bereishit and one for dvarim, but they only take out three.

Aryeh Shore