A translated version of the Columbus voyage log of 1492j may be found at
Medieval Sourcebook: Christopher Columbus: Extracts From Journal .

Assuming that Tishrei 1 could be postponed from 1 up to 6 days from the day of the molad of Tishrei, what then would be the length in days of the longest single Hebrew year?

The total number of ways in which 1 up to 6 weekdays may be selected for postponement purposes is 126.

Properties of Hebrew Year Periods - Part 1 indicates that without any of the dehiyyot, the longest single Hebrew year would be 384 days in length. However, by adding Dehiyyah Lo ADU Rosh, the longest single Hebrew year grows in length to 385 days.

For reasons which are presently quite obscure, it appears that as long as at least one weekday has been selected for the postponement of Tishrei, then no matter how many days (up to six), or whatever combination of weekdays are selected, the longest possible single Hebrew year will always be 385 days in length.

The Weekly Question will very much appreciate receiving any mathematical analysis of this rather intriguing Hebrew calendar phenomenon.

Assuming that Tishrei 1 could be postponed from 1 up to 6 days from the day of the molad of Tishrei, what then would be the length in days of the longest 12-month Hebrew year?

The total number of ways in which 1 up to 6 weekdays may be selected for postponement purposes is 126.

Properties of Hebrew Year Periods - Part 1 indicates that without any of the dehiyyot, the longest 12-month Hebrew year would be 355 days in length. However, by adding Dehiyyah Lo ADU Rosh, the longest 12-month Hebrew year grows in length to 356 days.

For reasons which are presently quite obscure, it appears that as long as at least two consecutive weekdays have been selected for the postponement of Tishrei, then no matter how many days (up to six), or whatever combination of weekdays are selected, the longest possible 12-month Hebrew year will always be 357 days in length.

However, when at least one or more non-consecutive weekdays are selected for the postponement of Tishrei, then the longest possible 12-month Hebrew year is 356 days in length.

The largest number of non-consecutive weekdays which can be selected from the seven weekdays is 3.

The Weekly Question will very much appreciate receiving any mathematical analysis of this rather intriguing Hebrew calendar phenomenon.

Correspondent Ben Dreyfus suggested the following answer.

I'm assuming from your answer to Question 243 that the postponement 
you're talking about is an extension of Lo ADU, saying that (e.g.) Rosh 
Hashanah must always be on Tuesday.  In that case, i'm going with 357 days 
(exactly 51 weeks) as the longest length of a 12-month year, just as 385 days 
(55 weeks) is the longest 13-month year.  (If there is only one day of the 
week when RH can fall, then every year must have an integer number of 
weeks.)

Ben Dreyfus

Assuming that Tishrei 1 could be postponed from 1 up to 6 days from the day of the molad of Tishrei, what then would be the length in days of the shortest 12-month Hebrew year?

The total number of ways in which 1 up to 6 weekdays may be selected for postponement purposes is 126.

Properties of Hebrew Year Periods - Part 1 indicates that without any of the dehiyyot, the shortest 12-month Hebrew year would be 354 days in length. However, by adding Dehiyyah Lo ADU Rosh, the shortest 12-month Hebrew year decreases in length to 352 days.

For reasons which are presently quite obscure, it appears that as long as at least four consecutive weekdays have been selected for the postponement of 1 Tishrei, then no matter how many days (up to six), or whatever combination of weekdays are selected, the shortest possible 12-month Hebrew year will always be 350 days in length.

The Weekly Question will very much appreciate receiving any mathematical analysis of this rather intriguing Hebrew calendar phenomenon.

Relative to 5766H (in 2005g), when last was Dehiyyah B'TU'TKPT invoked?

Dehiyyah B'TU'TKPT is invoked whenever the molad of Tishrei is found to be on, or past, 15h 589p, on a Monday immediately following a 13-month year. Whenever that condition occurs in the calculation of the molad of Tishrei, then the first day of Rosh HaShannah is postponed to Tuesday. This postponement increases to 383 days the length of the previous 13-month year. As a desirable consequence of this rule, the 382-day year that would otherwise be generated is entirely eliminated from the Hebrew calendar.

The molad of Tishrei 5766H is calculated as being 2d 16h 876p.

Since 5765H was a 13-month year, Dehiyyah BeTU'TeKaPoT is invoked, postponing Rosh HaShannah 5766H from Monday, the day of the molad of Tishrei 5766H, to Tuesday.

The Dehiyyot and The Qeviyyot show that Dehiyyah B'TU'TKPT is invoked a total of 3,712 times over the full Hebrew calendar cycle of 689,472 years.

That makes Dehiyyah B'TU'TKPT the least often used rule for postponing the first day of Rosh HaShannah.

Relative to 5766H (in 2005g), Dehiyyah B'TU'TKPT was last invoked for 1 Tishrei 5688H (Tue 27 Sep 1927g).

Relative to 5766H (in 2005g), when next will Dehiyyah B'TU'TKPT be invoked?

Dehiyyah B'TU'TKPT is invoked whenever the molad of Tishrei is found to be on, or past, 15h 589p, on a Monday immediately following a 13-month year. Whenever that condition occurs in the calculation of the molad of Tishrei, then the first day of Rosh HaShannah is postponed to Tuesday. This postponement increases to 383 days the length of the previous 13-month year. As a desirable consequence of this rule, the 382-day year that would otherwise be generated is entirely eliminated from the Hebrew calendar.

The molad of Tishrei 5766H is calculated as being 2d 16h 876p.

Since 5765H was a 13-month year, Dehiyyah BeTU'TeKaPoT is invoked, postponing Rosh HaShannah 5766H from Monday, the day of the molad of Tishrei 5766H, to Tuesday.

The Dehiyyot and The Qeviyyot show that Dehiyyah B'TU'TKPT is invoked a total of 3,712 times over the full Hebrew calendar cycle of 689,472 years.

That makes Dehiyyah B'TU'TKPT the least often used rule for postponing the first day of Rosh HaShannah.

Relative to 5766H (in 2005g), Dehiyyah B'TU'TKPT was last invoked 78 years ago for 1 Tishrei 5688H (Tue 27 Sep 1927g).

Relative to 5766H (in 2005g), Dehiyyah B'TU'TKPT will next be invoked 247 years from now for 1 Tishrei 6013H (Tue 5 Oct 2252g).

Incidentally, it is entirely coincidental that the answer to Weekly Question 247 happens to be "247 years from now".

The next question was asked and solved by correspondent Nachum Dershowitz.

How far apart can be two consecutive invocations of Dehiyyah B'TU'TKPT?

Dehiyyah B'TU'TKPT is invoked whenever the molad of Tishrei is found to be on, or past, 15h 589p, on a Monday immediately following a 13-month year. Whenever that condition occurs in the calculation of the molad of Tishrei, then the first day of Rosh HaShannah is postponed to Tuesday. This postponement increases to 383 days the length of the previous 13-month year. As a desirable consequence of this rule, the 382-day year that would otherwise be generated is entirely eliminated from the Hebrew calendar.

The molad of Tishrei 5766H is calculated as being 2d 16h 876p.

Since 5765H was a 13-month year, Dehiyyah BeTU'TeKaPoT is invoked, postponing Rosh HaShannah 5766H from Monday, the day of the molad of Tishrei 5766H, to Tuesday.

Relative to 5766H (in 2005g), Dehiyyah B'TU'TKPT was last invoked 78 years ago for 1 Tishrei 5688H (Tue 27 Sep 1927g), and will next be invoked 247 years from now for 1 Tishrei 6013H (Tue 5 Oct 2252g).

The Dehiyyot and The Qeviyyot show that Dehiyyah B'TU'TKPT is invoked a total of 3,712 times over the full Hebrew calendar cycle of 689,472 years.

That makes Dehiyyah B'TU'TKPT the least often used rule for postponing the first day of Rosh HaShannah.

Two consecutive invocations of Dehiyyah B'TU'TKPT can occur either 78, 98, 169, 247, or 345 years apart. The table demonstrates the frequencies of these occurences over the full Hebrew calendar cycle of 689,472 years.

Please note that the very last occurence of Dehiyyah B'TU'TKPT in the full Hebrew calendar cycle is separated by 247 years from its very first invocation in the second full Hebrew calendar cycle.

Assuming that no change ever takes place to any of the Hebrew, Gregorian, or Julian calendars, then the second full Hebrew calendar cycle theoretically begins at the start of Hebrew year 689,473H (Mon 4 Nov 685720g / 8 Oct 685706j).

Many thanks to correspondent Nachum Dershowitz for suggesting the question, and to both correspondents Nachum Dershowitz and Ari M. Brodsky for sharing their correct answers with the Weekly Question.

Between which pair of Hebrew years does each of the possible 5 B'TU'TKPT separations first occur?

Dehiyyah B'TU'TKPT is invoked whenever the molad of Tishrei is found to be on, or past, 15h 589p, on a Monday immediately following a 13-month year. Whenever that condition occurs in the calculation of the molad of Tishrei, then the first day of Rosh HaShannah is postponed to Tuesday. This postponement increases to 383 days the length of the previous 13-month year. As a desirable consequence of this rule, the 382-day year that would otherwise be generated is entirely eliminated from the Hebrew calendar.

The molad of Tishrei 5766H is calculated as being 2d 16h 876p.

Since 5765H was a 13-month year, Dehiyyah B'TU'TKPT is invoked, postponing Rosh HaShannah 5766H from Monday, the day of the molad of Tishrei 5766H, to Tuesday.

The Dehiyyot and The Qeviyyot show that Dehiyyah B'TU'TKPT is invoked a total of 3,712 times over the full Hebrew calendar cycle of 689,472 years.

That makes Dehiyyah B'TU'TKPT the least often used rule for postponing the first day of Rosh HaShannah.

Two consecutive invocations of Dehiyyah B'TU'TKPT can occur either 78, 98, 169, 247, or 345 years apart. The table demonstrates the frequencies of these occurences over the full Hebrew calendar cycle of 689,472 years, and also their first occurences during those years.

Correspondent Ari M. Brodsky shared a number of other interesting features pertaining to Hebrew year 5766H begun on Tuesday 4 October 2005g.

What are at least 3 other calendar oriented features relevant to Hebrew year 5766H?

Correspondent Ari M. Brodsky noted the following features relevant to Hebrew year 5766H (started Tue 4 Oct 2005g).

1) Beginning on Tuesday, the year is 354 days long causing its 12 months 
to alternate exactly between 30 and 29 day months. About 6.2% of all of the 
years in the full Hebrew calendar cycle of 689,472 years are 12-month years 
beginning on Tuesday.

2) Dechiyyah B'TU'TKPT postponed the beginning of 5766H.

3) For observant Jews living in Canada, there are no three consecutive working
days in October 2005g, due to the arrangement of the High Holiday Festivals 
and the fact that Thanksgiving falls during the same week as Yom Kippur.

4) We read from 3 Torah scrolls on Shabbat Rosh Hodesh Hanukka.  The
regular parsha that day is Mikketz, which is quite long as well.

5) There are only 6 days of Chanukka in 2005g.

6) 5766H is the 9th year of the 19-year Jewish calendar cycle GUChADZT.  Until
the end of Shevat 5766H (February 2006), we are within the “late-year”
period, when all Jewish calendar dates and holidays fall at their latest 
possible points in the solar year (i.e. relative to the civil calendar).

7) February 2006 does not contain the first day of any Jewish month.

8) All possible “double parashiyyot” are combined during 5766H.  As
well, Parashat Vayyeilekh will be read on two Shabbat mornings during 
the year – on the first Shabbat of the year (5 Tishrei / October 8, 2005g) 
and on the last Shabbat of the year (23 Elul / September 16, 2006g).

9) Yom HaAtzmaut is actually celebrated on 5 Iyyar, for a change.

10) There will be a discrepancy in Torah readings between Israel and 
the Diaspora, for several weeks after Shavuot, due to the second day of 
Shavuot falling on Shabbat.

11) On the evening of 4 Kislev, (December 4), Diaspora Jews begin
praying for rain.  That certainly makes for an exciting year!

Ari Brodsky

Thank you correspondent Ari M. Brodsky for sharing these wonderful observations.

The 7th fact notes that no Hebrew month begins in February 2006g, thereby suggesting the next question.

 First  Begun 21 Jun 1998 
First  Paged  2 Feb 2005
Next Revised 18 Dec 2005