Best Answer

11 December has had 56 Saturdays between 1600 and 2000 in the Gregorian calendar.

In the Gregorian calendar, centuries are leap years only if the year is divisible by 400, which means that 1700, 1800 and 1900 were not leap years.

Every year, the day of a date goes forward 1 day except in a leap year when it goes forward 2 days; this leads to cycle of 28 days that any date could have:

{Mo, Tu, We, Th}, {Sa, Su, Mo, Tu}, {Th, Fr, Sa, Su}, {Tu, We, Th, Fr}, {Su, Mo, Tu, We}, {Fr, Sa, Su, Mo}, {We, Th, Fr, Sa}

The list is in blocks of four that come between each leap year - each day of the week starts one of the blocks, and each day of the week occurs in each position in a block, one in each of fours block.

When a century is not a leap year, the sequence jumps forward 5 blocks instead of to the next block.

As a century (100 years) is divisible by 4, an exact number of blocks (100 ÷ 4 = 25) will occur within a year, and as we are interested only in Saturdays, the sequence of which blocks contain Saturday makes life easier: NYYNNYY

As 25 blocks will be used in any year, and there is a sequence of 7 blocks, they will all be used 3 times and the first 4 will be repeated at the end: 3 x 7 + 4 = 25.

If every century was a leap year, the sequence would continue across the centuries; however, with the Gregorian calendar centuries are only leap years if they are divisible by 400 - only 1 in every 4 century years is a leap year. As a result, the sequence will jump blocks at non-leap year centuries, as the next year's day for any given date is the one after the current day.

Looking at the full sequence above, it can be seen that when a non-leap year occurs, the sequence jumps an extra 4 blocks forward, making the next block 2 back from the current block.

Supposing we number the blocks 0, 1, ..., 6 with block 0 the first block used in 1600-1603. Then the sequence of blocks used in each century is:

1600s - 0123456 0123456 0123456 0123

1700s - 1234560 1234560 1234560 1234

1800s - 2345601 2345601 2345601 2345

1900s - 3456012 3456012 3456012 3456

2000s - 01234...

which means that each block of 4 centuries starting with a leap century

repeats the same sequence of the blocks, with each new century starting one block later.

One thing to note is when the block jump occurs. For Jan 1 to Feb 28 which are before the leap day (Feb 29), their blocks will run for the years 01-04, 05-08, ..., 97-00; and for those after the leap day, their blocks will run for the years 00-03, 04-07, ..., 96-99.

So now we are ready to find the number of Saturdays for 11 December for 1600-2000.

It is easier to work backwards from 2000 as the day for 11 December 2000 can easily be found.

11 December is after the leap day, so each block is used for years 00-03, 04-07, ..., 96-99. 2000 was a leap year, so no block jump occurs before it.

11 December 2000 was a Monday and is the first day of a block; using the blocks above it is in the first block, so let's number that block 0 and the rest 1-6 in order. Now, using the sequence above for the blocks used and whether they contain Saturdays, we can write out which blocks in 1600-2000 contains a Saturday. However, as each block is used 3 times there will be 3 x 4 = 12 Saturdays, plus however many Saturdays occur in the first 4 blocks of each century that are repeated; thus we need only note those 4 blocks:

1600s: NYYN - 2 Saturdays

1700s: YYNN - 2 Saturdays

1800s: YNNY - 2 Saturdays

1900s: NNYY - 2 Saturdays

An extra 8 Saturdays.

Which means there are 4 x 12 + 8 = 56 Saturdays.

Q: How often does December 11 fall on Saturday over the 400 year Gregorian calendar cycle from 1600 to 2000?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

The Gregorian reform contained two parts: a reform of the Juliancalendaras used prior to Pope Gregory XIII's time and a reform of the lunar cycle used by the Church, with the Julian calendar, to calculate the date of Easter

The Chinese calendar repeats after 12 years.

The Mayan calender had 13 months, one for each moon cycle.

30065

Cycle billing

Related questions

There are at least three Mayan calendars. The next 'Great Cycle' starts on 22nd December 2012 (Gregorian)

There are at least three Mayan calendars. The next 'Great Cycle' starts on 22nd December 2012 (Gregorian)

The Gregorian reform contained two parts: a reform of the Juliancalendaras used prior to Pope Gregory XIII's time and a reform of the lunar cycle used by the Church, with the Julian calendar, to calculate the date of Easter

Nothing causes the Mayan calendar to end it is just the end of one cycle and the start of another one. Much the same as the new year in the Gregorian calendar. It's just a longer cycle.

Its Gregorian dates are determined by the cycles of the Hebrew calendar, in which Hanukkah always starts on the 25th of kislev.

No, the Gregorian calendar is primarily based on the sun. It was introduced by Pope Gregory XIII in 1582 to reform the Julian calendar, which was based on the lunar cycle. The Gregorian calendar adjusted the length of the year to better align with the solar year.

The Gregorian and Hebrew calendars never coincide, but the Hebrew calendar does have a leap year system which is a 19 year cycle, designed to keep calendar in general sync with the solar year.

Because the Hebrew calendar is based on the lunar cycle, the dates of Jewish holidays according to the Gregorian calendar change from year to year. For this reason, the beginning of Hanukkah can range from late November to late December. In 2021, Hanukkah begins at sundown on Sunday, November 28, and continues through Monday, December 6.

The Muslim calendar, also known as the Islamic or Hijri calendar, is based on the lunar cycle and has 12 months in a year of 354 or 355 days. It is primarily used for religious purposes. The Gregorian calendar, which is the most widely used calendar in the world, is a solar calendar with 12 months in a year of 365 or 366 days. It is a standard calendar for civil purposes.

Inca(or maya) on their calender it says that the end of the world is 21/12/12. It is the end of 'The Great Cycle' in their calendar but it has no more significance than the end of a millennium in our present, Gregorian, calendar

The Chinese calendar is a lunar calendar, which is based on the moons cycle. Chinese new year falls between January 21 and February 19. The next Chinese year will be cycle 78, year 28, the year of the hare and will begin on Gregorian February 3 2011

The Islamic calendar is lunar, which means it's based on the phases of the moon. It is either 354 or 355 days long, and began in the year 622 CE when the Prophet Muhammad migrated from Mecca to Medina. The Gregorian calendar is solar. It is about 365 days long, and numbers 0 CE at the birth of Jesus. It is a reform of the Julian calendar as used up to Pope Gregory's time, together with a reform of the lunar cycle used by the Church along with the Julian calendar for calculating dates of Easter.