I am doing a lecture on the math of the Jewish calendar. I understand the concepts of the 3 types of year lengths - maleh, chaser and kesidrah - "full", "regular" and "deficient" years. I also understand the 4 postponement rules for Rosh Hashannah. (I say this, to avoid answers or comments that attempt to just state the rules.) My question is specifically why if Pesach falls on Tues., Thurs., or Shabbat, these days can be repeated the following year (when the following year is a leap year - maleh), but Sunday is never repeated (i.e it is never followed by a leap year - maleh)?
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1How do you know it's not?– YpnypnMay 2, 2014 at 16:24
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1 Answer
When Pesach falls on Sunday, the following Rosh Hashana will be Tuesday (163 days = 23 weeks + 2 days). When Rosh Hashanah falls on Tuesday that year will always be kisidran (Rambam Hilchos Kiddush Hachodesh 8:10)
We now explain mathematically why that is true in your case when the next year is a leap year. When Rosh Hashanah falls on Tuesday, the molad must have fallen Monday afternoon through Tuesday afternoon (molad zaken rule). When adding 5:21:589 (the delta between RH molads for a leap year) the range of molads for the next year is Sunday 15 hours, 589 cheleks - Monday 15 h, 589 c. Thus the next RH will be on Monday and the current years has a shift of 6 days.
Since a leap year has either 383, 384 or 385 days dependent on whether it is deficient, regular or full causing the following year to shift by 5,6 or 0 days, respectively, the year must be a 384 day year = regular (kesidran)
See Peirush on Rambam ibid for a complete analysis of all legal combinations of days and year types.
