When next will

Birkat HaHamah(the blessing of the sun) not be recited in the Hebrew month ofNisan?

** Birkat HaHamah** (the Blessing of the Sun) is recited

Correspondent **Robert H. Douglass** not only * asked*, but also

He calculated that the next time *Birkat HaHamah* would not be recited in the Hebrew month of ** Nisan** would be on

Thank you **Robert H. Douglass** for your thought provoking questions and for sharing with us the results of your very interesting research into the calendar.

** Weekly Question 162** deals with a hypothetical calendar organizational problem that shows one of the effects of the

Which day, or days, of the week would have begun 356 and 382 day years had Friday been the only day disallowed for 1

Tishrei?

Had ** Friday** been the only day disallowed for

Referring to Properties of Hebrew Year Periods - Part 1, the answer can be developed analytically as shown below.

Letw =the weekday disallowed for1. LetTishreiM + m = 354d 8h 876pandL = 356d.Then

L = D" - D' = 354d + [f + m] + p" - p' = 356d. (Equation 4.5) Hence,[f + m] + p" - p' = 356d - 354d = 2d. Consequently, it is necessary thatp" = 1d.Leading to

D" = w + p" = w + 1d. Hence,w + 1d - D' = 356dD' = w - 355dD' MOD 7d = (w - 355d) MOD 7d = (w - 5d) MOD 7d = (w + 2d) MOD 7d

Therefore, given the single non-allowable weekday **w**, the **356 day year** will begin on **D' = w + 2d** and end on **D" = w + 1d**.

In the above example, with ** Friday** removed, the

The same analysis can be applied in the case of the **382 day year**.

Letw =the weekday disallowed for1. LetTishreiM + m = 383d 21h 589pandL = 382d.Then

L = D" - D' = 383d + [f + m] + p" - p' = 382d. (Equation 4.5) Hence,[f + m] + p" - p' = 382d - 383d = -1d. Consequently, it is necessary thatp' = 1d.Leading to

D' = w + p' = w + 1d. Hence,D" - w - 1d = 382dD" = w + 383dD" MOD 7d = (w + 383d) MOD 7d = (w + 5d) MOD 7d = (w - 2d) MOD 7d

Therefore, given the single non-allowable weekday **w**, the **382 day year** will begin on **D' = w + 1d** and end on **D" = w - 2d**.

In the above example, with ** Friday** removed, the

The * keviyot* for a calendar, missing only

YEAR LENGTH IN DAYS | |||||||||
---|---|---|---|---|---|---|---|---|---|

DAY | 353 | 354 | 355 | 356 | 382 | 383 | 384 | 385 | TOTALS |

Sun | 0 | 39369 | 0 | 22839 | 0 | 0 | 36288 | 0 | 98496 |

Mon | 0 | 0 | 62208 | 0 | 0 | 3712 | 32576 | 0 | 98496 |

Tue | 0 | 39369 | 22839 | 0 | 0 | 3712 | 32576 | 0 | 98496 |

Wed | 0 | 39369 | 22839 | 0 | 0 | 3712 | 32576 | 0 | 98496 |

Thu | 0 | 39369 | 22839 | 0 | 0 | 3712 | 32576 | 0 | 98496 |

Sat | 39369 | 62208 | 22839 | 0 | 3712 | 36288 | 0 | 32576 | 196992 |

TOTALS | 39369 | 219684 | 153564 | 22839 | 3712 | 51136 | 166592 | 32576 | 689472 |

Part of the answer to ** Weekly Question 163** may be derived from

Which day, or days, of the week would have begun 356 and 382 day years had

Tuesday,Thursday, andShabbatbeen disallowed for 1Tishrei?

Had *Tuesday*, *Thursday*, and *Shabbat* been disallowed for **1 Tishrei**,then the

Referring to Properties of Hebrew Year Periods - Part 1, the answer can be developed analytically as shown below.

Letw =the weekday disallowed for1. LetTishreiM + m = 354d 8h 876pandL = 356d.Then

L = D" - D' = 354d + [f + m] + p" - p' = 356d. (Equation 4.5) Hence,[f + m] + p" - p' = 356d - 354d = 2d. Consequently, it is necessary thatp" = 1d.Leading to

D" = w + p" = w + 1d. Hence,w + 1d - D' = 356dD' = w - 355dD' MOD 7d = (w - 355d) MOD 7d = (w - 5d) MOD 7d = (w + 2d) MOD 7d

Therefore, given the single non-allowable weekday **w**, the **356 day year** will begin on **D' = w + 2d** and end on **D" = w + 1d**.

In the above example, with ** Friday** removed, the

The same analysis can be applied in the case of the **382 day year**.

Letw =the weekday disallowed for1. LetTishreiM + m = 383d 21h 589pandL = 382d.Then

L = D" - D' = 383d + [f + m] + p" - p' = 382d. (Equation 4.5) Hence,[f + m] + p" - p' = 382d - 383d = -1d. Consequently, it is necessary thatp' = 1d.Leading to

D' = w + p' = w + 1d. Hence,D" - w - 1d = 382dD" = w + 383dD" MOD 7d = (w + 383d) MOD 7d = (w + 5d) MOD 7d = (w - 2d) MOD 7d

Therefore, given the single non-allowable weekday **w**, the **382 day year** will begin on **D' = w + 1d** and end on **D" = w - 2d**.

Given that some weekday **w** must be bypassed for the weekday of **1 Tishrei**, it is possible to relate to

356 DAY YEAR | 382 DAY YEAR | |||
---|---|---|---|---|

DAY | START | END | START | END |

w | w + 2d | w + 1d | w + 1d | w - 2d |

If the postponement days are given as **w, w + 2d, and w + 4d** then, according to the relationships tabulated above, the starts and ends of the **356 and 382 day years** may be tabulated as follows:

356 DAY YEAR | 382 DAY YEAR | |||
---|---|---|---|---|

DAY | START | END | START | END |

w | w + 2d | w + 1d | w + 1d | w - 2d |

w + 2d | w + 4d | w + 3d | w + 3d | w |

w + 4d | w + 6d | w + 5d | w + 5d | w + 2d |

The tabulation shows that in this situation, only **w + 6d** can start a **356 day** year, because **w + 2d** and **w + 4d** have been disallowed for year starts.

The table also shows that the only allowable start day for the **382 day** year is **w + 1d**, because days **w** and **w + 2d**, the end days of the **382 day year**, are not permitted to start any year in this example.

Thus, when **w = 3 (Tue), then w + 2d = 5d (Thu), and w + 4d = 7d ( Shabbat)**.

Hence, the start of the **356 day year**, given by **w + 6d MOD 7d = 2d**, is ** Monday**.

Similarly, the start of the **382 day year**, given by **w + 1d = 4d**, is ** Wednesday**.

The following table shows the distibution of the year lengths over the full Hebrew calendar cycle of **689,472 years** when ** Tuesday, Thursday, and Shabbat** are not permitted week days for

YEAR LENGTH IN DAYS | |||||||||
---|---|---|---|---|---|---|---|---|---|

DAY | 353 | 354 | 355 | 356 | 382 | 383 | 384 | 385 | TOTALS |

Sun | 39369 | 0 | 85047 | 0 | 0 | 40000 | 0 | 32576 | 196992 |

Mon | 0 | 39369 | 0 | 22839 | 0 | 0 | 36288 | 0 | 98496 |

Wed | 0 | 101577 | 22839 | 0 | 3712 | 36288 | 0 | 32576 | 196992 |

Fri | 39369 | 0 | 85047 | 0 | 0 | 40000 | 0 | 32576 | 196992 |

TOTALS | 78738 | 140946 | 192933 | 22839 | 3712 | 116288 | 36288 | 97728 | 689472 |

It may be noted that when **w = 4d (Wed)**, then **w + 2d = 6d (Fri)**, and **w + 4d MOD 7d = 1d (Sun)**, which actually are the days specified for ** Dehiyah Lo ADU Rosh**. Not too surprisingly, when

What would have been the single year lengths had

Shabbatbeen the only day allowed to startRosh Hashannah?

When the postponements allowed are only **one day**, then the single year lengths can be either **353, 354, 355, 356, 382, 383, 384, or 385 days**. The following tables, derived for the full Hebrew calendar cycle of **689472 years**, represent the smallest number of weekday combinations needed to show all of the possible ways in which **one day** postponements can be designated.

YEAR LENGTH IN DAYS | |||||||||
---|---|---|---|---|---|---|---|---|---|

DAY | 353 | 354 | 355 | 356 | 382 | 383 | 384 | 385 | TOTALS |

Mon | 39369 | 62208 | 22839 | 0 | 3712 | 36288 | 0 | 32576 | 196992 |

Tue | 0 | 39369 | 0 | 22839 | 0 | 0 | 36288 | 0 | 98496 |

Wed | 0 | 0 | 62208 | 0 | 0 | 3712 | 32576 | 0 | 98496 |

Thu | 0 | 39369 | 22839 | 0 | 0 | 3712 | 32576 | 0 | 98496 |

Fri | 0 | 39369 | 22839 | 0 | 0 | 3712 | 32576 | 0 | 98496 |

Sat | 0 | 39369 | 22839 | 0 | 0 | 3712 | 32576 | 0 | 98496 |

TOTALS | 39369 | 219684 | 153564 | 22839 | 3712 | 51136 | 166592 | 32576 | 689472 |

YEAR LENGTH IN DAYS | |||||||||
---|---|---|---|---|---|---|---|---|---|

DAY | 353 | 354 | 355 | 356 | 382 | 383 | 384 | 385 | TOTALS |

Mon | 39369 | 62208 | 22839 | 0 | 3712 | 36288 | 0 | 32576 | 196992 |

Wed | 39369 | 0 | 85047 | 0 | 0 | 40000 | 0 | 32576 | 196992 |

Thu | 0 | 39369 | 0 | 22839 | 0 | 0 | 36288 | 0 | 98496 |

Fri | 0 | 0 | 62208 | 0 | 0 | 3712 | 32576 | 0 | 98496 |

Sat | 0 | 39369 | 22839 | 0 | 0 | 3712 | 32576 | 0 | 98496 |

TOTALS | 78738 | 140946 | 192933 | 22839 | 3712 | 83712 | 101440 | 65152 | 689472 |

YEAR LENGTH IN DAYS | |||||||||
---|---|---|---|---|---|---|---|---|---|

DAY | 353 | 354 | 355 | 356 | 382 | 383 | 384 | 385 | TOTALS |

Mon | 39369 | 62208 | 22839 | 0 | 3712 | 36288 | 0 | 32576 | 196992 |

Tue | 0 | 39369 | 0 | 22839 | 0 | 0 | 36288 | 0 | 98496 |

Thu | 0 | 101577 | 22839 | 0 | 3712 | 36288 | 0 | 32576 | 196992 |

Fri | 0 | 39369 | 0 | 22839 | 0 | 0 | 36288 | 0 | 98496 |

Sat | 0 | 0 | 62208 | 0 | 0 | 3712 | 32576 | 0 | 98496 |

TOTALS | 39369 | 242523 | 107886 | 45678 | 7424 | 76288 | 105152 | 65152 | 689472 |

YEAR LENGTH IN DAYS | |||||||||
---|---|---|---|---|---|---|---|---|---|

DAY | 353 | 354 | 355 | 356 | 382 | 383 | 384 | 385 | TOTALS |

Mon | 0 | 101577 | 22839 | 0 | 3712 | 36288 | 0 | 32576 | 196992 |

Wed | 39369 | 0 | 85047 | 0 | 0 | 40000 | 0 | 32576 | 196992 |

Fri | 39369 | 0 | 85047 | 0 | 0 | 40000 | 0 | 32576 | 196992 |

Sat | 0 | 39369 | 0 | 22839 | 0 | 0 | 36288 | 0 | 98496 |

TOTALS | 78738 | 140946 | 192933 | 22839 | 3712 | 116288 | 36288 | 97728 | 689472 |

In each of the above tables, it is to be noted that the postponements called for are at most **one day**. Also to be noted, is that the effect of prohibiting *Rosh Hashannah* starts on ** Sunday, Tuesday, and Thursday**, is

YEAR LENGTH IN DAYS | |||||||||
---|---|---|---|---|---|---|---|---|---|

DAY | 353 | 354 | 355 | 356 | 382 | 383 | 384 | 385 | TOTALS |

Mon | 39369 | 0 | 85047 | 0 | 0 | 40000 | 0 | 32576 | 196992 |

Tue | 0 | 39369 | 0 | 22839 | 0 | 0 | 36288 | 0 | 98496 |

Thu | 0 | 101577 | 22839 | 0 | 3712 | 36288 | 0 | 32576 | 196992 |

Sat | 39369 | 0 | 85047 | 0 | 0 | 40000 | 0 | 32576 | 196992 |

TOTALS | 78738 | 140946 | 192933 | 22839 | 3712 | 116288 | 36288 | 97728 | 689472 |

When ** Shabbat** is the only day allowed to start

Consequently, under this restriction, the single year lengths can only be either **350, 357, 378, or 385 days** long. When ** Shabbat** is the only day allowed to start

YEAR LENGTH IN DAYS | |||||
---|---|---|---|---|---|

DAY | 350 | 357 | 378 | 385 | TOTALS |

Shabbat |
163785 | 271671 | 40000 | 214016 | 689472 |

TOTALS | 163785 | 271671 | 40000 | 214016 | 689472 |

** Weekly Question 164** introduced the idea that the effect of prohibiting

What is the smallest number of weekday combinations needed in order to view all of the possible

single yearstatistical distributions when up to 6 weekdays may be disallowed for 1Tishrei?

Suppose that the days disallowed for **1 Tishrei** are

These weekdays are expressed numerically as **1, 3, and 5** respectively. The statistical effect, over the full Hebrew calendar cycle of **689,472 years**, of these implied postponements may be tabulated as follows:-

YEAR LENGTH IN DAYS | |||||||||
---|---|---|---|---|---|---|---|---|---|

DAY | 353 | 354 | 355 | 356 | 382 | 383 | 384 | 385 | TOTALS |

Mon | 0 | 101577 | 22839 | 0 | 3712 | 36288 | 0 | 32576 | 196992 |

Wed | 39369 | 0 | 85047 | 0 | 0 | 40000 | 0 | 32576 | 196992 |

Fri | 39369 | 0 | 85047 | 0 | 0 | 40000 | 0 | 32576 | 196992 |

Sat | 0 | 39369 | 0 | 22839 | 0 | 0 | 36288 | 0 | 98496 |

TOTALS | 78738 | 140946 | 192933 | 22839 | 3712 | 116288 | 36288 | 97728 | 689472 |

Having developed these statistical distributions, it is no longer necessary to work out any other combination of **3 days** whose selection is derived by adding exactly the same number to each of the originally forbidden **3 days**.

The **7 combinations** which are derived from **1, 3, and 5** are

Week Days | |
---|---|

+0 | 1, 3, 5 |

+1 | 2, 4, 6 |

+2 | 3, 5, 0 |

+3 | 4, 6, 1 |

+4 | 5, 0, 2 |

+5 | 6, 1, 3 |

+6 | 0, 2, 4 |

All of these combinations will produce the statistical distributions that are mathematically equivalent to the effects of forbidding **1 Tishrei** on week days

For example, combination **4, 6, 1** (**+3** above) represents the week days that are used in * Dehiyah Lo ADU Rosh*. Adding

YEAR LENGTH IN DAYS | |||||||||
---|---|---|---|---|---|---|---|---|---|

DAY | 353 | 354 | 355 | 356 | 382 | 383 | 384 | 385 | TOTALS |

Mon | 39369 | 0 | 85047 | 0 | 0 | 40000 | 0 | 32576 | 196992 |

Tue | 0 | 39369 | 0 | 22839 | 0 | 0 | 36288 | 0 | 98496 |

Thu | 0 | 101577 | 22839 | 0 | 3712 | 36288 | 0 | 32576 | 196992 |

Sat | 39369 | 0 | 85047 | 0 | 0 | 40000 | 0 | 32576 | 196992 |

TOTALS | 78738 | 140946 | 192933 | 22839 | 3712 | 116288 | 36288 | 97728 | 689472 |

The number of ways that **1 up to 6 days** may be chosen from the week, is ** 126**. Since

Combinations | |
---|---|

1 | 1 |

2 | 1, 2 |

3 | 1, 3 |

4 | 1, 2, 3 |

5 | 1, 4 |

6 | 1, 2, 4 |

7 | 1, 3, 4 |

8 | 1, 2, 3, 4 |

9 | 1, 2, 5 |

10 | 1, 3, 5 |

11 | 1, 2, 3, 5 |

12 | 1, 2, 4, 5 |

13 | 1, 3, 4, 5 |

14 | 1, 2, 3, 4, 5 |

15 | 1, 2, 4, 6 |

16 | 1, 2, 3, 4, 6 |

17 | 1, 2, 3, 5, 6 |

18 | 1, 2, 3, 4, 5, 6 |

One of the weekly scriptural readings during this time of year is the double portion known as ** Matot-Masei**. These portions are

The following question first appeared as ** Weekly Question 132**.

How often are the *Parshiot* * Matot* and

The *Parshiot* * Matot* and

This happens **72,576 times** over the full Hebrew calendar cycle of
**689,472 years** or

exactly **2 out of 19 times**.

One of the more prevalent practices, among the Jewish people, is that of reading the entire Mosaic text of their scriptures (Torah) over the course of one Hebrew year. At Simchat Torah, the last few verses are read, and then the entire cycle is repeated once again from Bereshit (Genesis).

The scriptural readings are divided into contiguous weekly portions, which
are read in their entirety each Shabbat morning. Each division is known as
a ** Parshah** or

Each portion is given a special name. Two portions that are
normally read together are ** Matot** and

These portions are ** Numbers 30:2 to 32:42** and

Occasionally, these two portions are read ** separately**,
rather than

Since there are **14 ways** of laying out the Hebrew years
(**14 keviyyot**), there
exist only

That source shows that the portions ** Matot** and

The Keviyyot shows the statistical distribution
of all the **leap years** that begin on **Thursday** in the
full Hebrew calendar cycle of **689,472 years**.

YEAR LENGTH IN DAYS | |||||||
---|---|---|---|---|---|---|---|

DAY | 353 | 354 | 355 | 383 | 384 | 385 | TOTALS |

Mon | 39369 | 0 | 81335 | 40000 | 0 | 32576 | 193280 |

Tue | 0 | 43081 | 0 | 0 | 36288 | 0 | 79369 |

Thu | 0 | 124416 | 22839 | 26677 | 0 | 45899 | 219831 |

Sat | 29853 | 0 | 94563 | 40000 | 0 | 32576 | 196992 |

TOTALS | 69222 | 167497 | 198737 | 106677 | 36288 | 111051 | 689472 |

Given this question, a number of correspondents wanted to know the most
recent separate readings of these two ** Parshiyot**.

The following question first appeared as ** Weekly Question 133**.

When was the most recent separate readings of

ParshiotandMatotand when will this next happen?Masei

One of the more prevalent practices, among the Jewish people, is that of
reading the entire Mosaic text of their scriptures (** Torah**) over the course of one Hebrew year. At

The scriptural readings are divided into contiguous weekly portions, which
are read in their entirety each ** Shabbat** morning. Each division is known as a

Each portion is given a special name. Two portions that are
normally read together are ** Matot** and

These portions are ** Numbers 30:2 to 32:42** and

The *Parshiot* * Matot* and

This happens **72,576 times** over the full Hebrew calendar cycle of
**689,472 years** or exactly **2 out of 19 times**.

The last time that each of these portions was read by themselves on
**2** separate *Shabbatot* occurred on the
**21st and 28th Tammuz 5744H** corresponding coincidentally to the

The next time that each of these portions will be read entirely on
**2** separate *Shabbatot* is the

**23 Tammuz 5765H** and

Correspondents **Larry Padwa, Ram Sinclair, Winfried Gerum, and Robert H. Douglass** found the correct Hebrew years in answer to this question.

Correspondent **Larry Padwa** remarked that

The last leap year that began on Thursday was 5744H, so the last time that they were read separately was in 1984g. The next occurrence will be in 5765H (2005g).

Correspondent **Ram Sinclair** stated that

The last and next occurrences of a leap year's Rosh-Hashannah on Thursday are September 8, 1983g; and September 16, 2004g respectively.Correspondent

Q133 is really simple: The last leap year commencing on a Thursday was 5744H (1983-09-08) The next such years are 5765H (2004-09-16) 5768H (2007-09-13) 5771H (2010-09-09) 5774H (2013-09-05) One might ask, how these years are distributed. Such years recur after 3,10,11,13,14,21 or 24 years. Surprisingly the three year interval is quite frequent (48.72%)! The next short span is 5765-5768. But occassionaly one has to wait 24 years between two such years. The next long wait is 5923-5947

Correspondent **Robert H. Douglass** stated that

Thank you correspondentsThis was explained in the current weekly question as: "the portions Matot and Masei are read separately only in leap years that begin on Thursday." The most recent time this occurred was HY 5744, a leap year of 385 days beginning on Thursday, September 8, 1983 CE. The next time this will occur is HY 5765, a leap year of 383 days beginning on Thursday, September 16, 2004 CE.

Why is it easy to count mentally the days from

Rosh Hashannah5663H toRosh Hashannah5763H?

The Gregorian calendar dates for these two year beginnings provides a clue.

** Rosh Hashannah 5663H** began on

Since the year **2000g** was a Gregorian **leap year**,

the **100** Gregorian years from **1902g** to **2002g** had **365 * 100 + 25 days = 36,525 days**.

Since **Sep 7** is **25 days** earlier than **Oct 2**,

the span from **Thu 2 Oct 1902g** to **Sat 7 Sep 2002g** is **36,525 - 25 = 36,500 days** long.

Consequently, the **100** Hebrew years beginning on ** Rosh Hashannah 5663H** were exactly

When next, at

Rosh Hashannah, will a 100th Hebrew anniversary be exactly 36,500 days long?

The next Hebrew centennial to have exactly **36,500 days** at ** Rosh Hashannah** will be marked at the start of

** Rosh Hashannah 5671H** began on

Since the year **2000g** was a Gregorian **leap year**,

the **100** Gregorian years from **1910g** to **2010g** had **365 * 100 + 25 days = 36,525 days**.

Since **Sep 9** is **25 days** earlier than **Oct 4**,

the span from **Tue 4 Oct 1910g** to **Thu 9 Sep 2010g** is **36,525 - 25 = 36,500 days** long.

Consequently, the **100** Hebrew years beginning on ** Rosh Hashannah 5671H** will be exactly

Correspondent **Robert H. Douglass** wasted no time in responding with the correct answer.

That would be Hebrew Year 5771, beginning on Thursday, Sept. 9, 2010... exactly 36500 days after the start of Hebrew Year 5671 on Tuesday, Oct. 4, 1910. Regards, Robert H. Douglass

Thank you **Robert H. Douglass** for your very prompt and correct answer to the question.

To get the greatest number possible of year lengths, which days of the week would have to be forbidden for 1

Tishrei?

The **greatest** number of year lengths that ** Dehiyot** can produce is

The ** 12** year lengths are generated whenever any

This is illustrated over the complete Hebrew calendar cycle of **689472 years** in the following statistical tabulation which eliminates ** Sunday, Monday, and Tuesday** from starting

YEAR LENGTH IN DAYS | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

DAY | 351 | 352 | 353 | 354 | 355 | 356 | 357 | 380 | 381 | 383 | 384 | 385 | TOTALS |

Wed | 39369 | 62208 | 62208 | 0 | 0 | 0 | 85047 | 3712 | 36288 | 0 | 0 | 105152 | 393984 |

Thu | 0 | 0 | 0 | 0 | 0 | 62208 | 0 | 0 | 0 | 0 | 36288 | 0 | 98496 |

Fri | 0 | 0 | 0 | 0 | 62208 | 0 | 0 | 0 | 0 | 3712 | 32576 | 0 | 98496 |

Sat | 0 | 0 | 0 | 39369 | 22839 | 0 | 0 | 0 | 0 | 3712 | 32576 | 0 | 98496 |

TOTALS | 39369 | 62208 | 62208 | 39369 | 85047 | 62208 | 85047 | 3712 | 36288 | 7424 | 101440 | 105152 | 689472 |

It is interesting to note that, when **3 consecutive** weekdays are forbidden from starting

To get the shortest possible 13 month year length, which day, or days, of the week would have to be forbidden for 1

Tishrei?

To get the ** shortest** possible

When at least **5** consecutive week days are forbidden for **1 Tishrei**, then the shortest 13 month year length possible is

This is illustrated over the complete Hebrew calendar cycle of **689472 years** in the following statistical tabulations which allow either only ** Friday and Shabbat**, or

YEAR LENGTH IN DAYS | |||||||||
---|---|---|---|---|---|---|---|---|---|

DAY | 350 | 351 | 356 | 357 | 378 | 379 | 384 | 385 | TOTALS |

Fri | 101577 | 62208 | 0 | 209463 | 3712 | 36288 | 0 | 177728 | 590976 |

Sat | 0 | 0 | 62208 | 0 | 0 | 0 | 36288 | 0 | 98496 |

TOTALS | 101577 | 62208 | 62208 | 209463 | 3712 | 36288 | 36288 | 177728 | 689472 |

YEAR LENGTH IN DAYS | |||||
---|---|---|---|---|---|

DAY | 350 | 357 | 378 | 385 | TOTALS |

Sat | 163785 | 271671 | 40000 | 214016 | 689472 |

TOTALS | 163785 | 271671 | 40000 | 214016 | 689472 |

The ** shortest** year length possible, whenever a certain number of week days are forbidden for

To generate the shortest possible year length, which day, or days, of the week would have to be forbidden for 1

Tishrei?

The ** shortest** year length possible, whenever a certain number of week days are forbidden for

To get the ** shortest** possible

This is illustrated over the complete Hebrew calendar cycle of **689,472 years** in the following statistical tabulations which forbid at least **4 consecutive weekdays** to start

YEAR LENGTH IN DAYS | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

DAY | 350 | 351 | 352 | 355 | 356 | 357 | 379 | 380 | 383 | 384 | 385 | TOTALS |

Thu | 39369 | 62208 | 62208 | 0 | 0 | 147255 | 3712 | 36288 | 0 | 0 | 141440 | 492480 |

Fri | 0 | 0 | 0 | 0 | 62208 | 0 | 0 | 0 | 0 | 36288 | 0 | 98496 |

Sat | 0 | 0 | 0 | 62208 | 0 | 0 | 0 | 0 | 3712 | 32576 | 0 | 98496 |

TOTALS | 39369 | 62208 | 62208 | 62208 | 62208 | 147255 | 3712 | 36288 | 3712 | 68864 | 141440 | 689472 |

YEAR LENGTH IN DAYS | |||||||||
---|---|---|---|---|---|---|---|---|---|

DAY | 350 | 351 | 356 | 357 | 378 | 379 | 384 | 385 | TOTALS |

Fri | 101577 | 62208 | 0 | 209463 | 3712 | 36288 | 0 | 177728 | 590976 |

Sat | 0 | 0 | 62208 | 0 | 0 | 0 | 36288 | 0 | 98496 |

TOTALS | 101577 | 62208 | 62208 | 209463 | 3712 | 36288 | 36288 | 177728 | 689472 |

YEAR LENGTH IN DAYS | ||||||||
---|---|---|---|---|---|---|---|---|

DAY | 350 | 352 | 355 | 357 | 380 | 383 | 385 | TOTALS |

Thu | 39369 | 124416 | 0 | 147255 | 40000 | 0 | 141440 | 492480 |

Sat | 0 | 0 | 124416 | 0 | 0 | 40000 | 32576 | 196992 |

TOTALS | 39369 | 124416 | 124416 | 147255 | 40000 | 40000 | 174016 | 689472 |

YEAR LENGTH IN DAYS | |||||
---|---|---|---|---|---|

DAY | 350 | 357 | 378 | 385 | TOTALS |

Sat | 163785 | 271671 | 40000 | 214016 | 689472 |

TOTALS | 163785 | 271671 | 40000 | 214016 | 689472 |

The next Hebrew year will be Hebrew year **5763H** beginning on ** Shabbat 7 September 2002g**. This year will be

First Begun 21 Jun 1998 First Paged 2 Jan 2005 Next Revised 2 Jan 2005