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Re: Fifth night of Chanukah

avrohom adler asked:

Notes:

1.      Malei + Leap Year =    Day this year equals day next year
K'sidran + Leap Year = 6 days later next year
Chaser + Leap Year = 5 days later next year

2.      Malei =    5 days later next year
K'sdran = 4 days later next year
Chaser = 3 days later next year

3.      We prefer a year to be K'sidran over Malei so we don't push
off Yom Tovim the next year.

4.      The following are the number of days between Rosh Hashana and
29 Kislev:

Chaser or K'sidran = 88
Malei = 89

5.      Each day is assigned a number as follows:

Sun=1, M=2, Tu=3, W=4, Th=5, F=6, Sa=7

6.      Rosh Hashana can be the following: 2,3,5,7
Hoshana Raba can be the following: 1,2,4,6
Yom Kippur can NOT be 1, 6

7.      In a Malei year, there are 287 days between 29 Kislev this
year, and Hoshana Raba the next year.

8.      In a Malei Leap Year, there are 297 days between 29 Kislev
and Rosh Hashana of the next year.

Cases:

Case #1: Any Chaser or K'sidran year

There are 88 days between Rosh Hashana and 29 Kislev. If 29 Kislev is
Shabbat, then Rosh Hashana would have been Wednesday. (88 days
divided by 7 leaves 4 days left over. 7,6,5,4 shows Rosh Hashana
lands on Wednesday) If Rosh Hashana falls on Wednesday then 10 days
later would land Yom Kippur on Friday. Since Yom Kippur can't fall on
Friday, then the 5th night of Chanukah can't be on Shabbat.

Case#2: Regular Malei year

We noted above that in a Malei year, there are 287 days between 29
Kislev and Hoshana Raba the next year. If we divide 287 (the total
number of days) by 7 (number of days in a week) we end up with a
remainder of 0. This means that which ever day of the week 29 Kislev
is this year  Hoshana Raba will fall on that day next year. Since
Hoshana Raba can't fall on Shabbat, then 29 Kislev also can't fall on Shabbat.

Case#3: Leap Year

A leap year has three possible amounts of days 383, 384, 385. If the
year has 383 or 384 (K'sidran or chaser) then we apply case #1, and
29 Kislev can't be on Shabbat. The last case is when we have a Malei
leap year with 385 days. Initially, this would allow us to have 29
Kislev be on Shabbat and Rosh Hashana of the following year would
fall on a Tuesday (there are 297 days between 29 Kislev and Rosh
Hashana of the following year. 297 divided by 7 leaves three days
left over, which would land Rosh Hashana on Tuesday). The problem
lies in the fact that if we made the year K'sidran,(384 days dived by
7 leaves 2 days left over) then Rosh Hashana would fall on Monday,
also an acceptable day of the week. Rambam brings down that we always
try to keep the calendar K'sidran when possible. Additionally, Rambam
notes that by keeping the calendar Malei, we would be pushing off
Rosh Hashana an extra day, which is not desirable.

avrohom adler, usa


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