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doug sinclair
12-07-2013, 12:24 AM
A friend pointed out to me recently, that August, 2014, has 5 Fridays, 5 Saturdays, and 5 Sundays. This phenomenon (according to his sources) only happens once every 750 years or so! Am I nuts for posting this, or could this actually be true?

MartyR
12-07-2013, 01:24 AM
Either way I think you're nuts :excited:

Every 31 day month has five of three consecutive days, so whether those are Monday/Tuesday/Wednesday or Friday/Saturday/Sunday doesn't seem to matter much to me ??? Basically, for a month to have three Fri/Sat/Suns it must be a 31 day month (of which there are seven) and the first day of the month must fall on Friday.

Each year except leap years contains 52 weeks and a day, so for three years in four the first day in a month moves forward by one, and then in a leap year it skips forward an extra one. So to take your example, August 1st is :

2014 Friday
2015 Saturday
2016 Monday (leap year)
2017 Tuesday
2018 Wednesday
2019 Thursday
2020 Saturday (leap year)
2021 Sunday
2022 Monday
2023 Tuesday
2024 Thursday (leap year)
2025 Friday

So you've been misinformed - it will be just 11 years before the next one :whistle:

There is no simple formula, which is almost always the case when you talk about calendars. But if you think our solar calendar is complicated, you should try looking at the lunar one :o

May 2015 is a 3-Fri/Sat/Sun month, and that will take only 5 years to occur again in 2020. It all depends on which year in the cycle of four the first day of the month falls on Friday.

Each month "behaves" differently depending on how many 30 day months precede it in a year, and January is a general exception because the skip forward of one day occurs in the year after the leap year and not in the leap year itself. The number of years in the cycle varies year on year for each month, and I believe the minimum lenth of the cyle is 5 years and the maximum 11 years.

I can't believe I just spent 10 minutes working this out, so I guess I must be nuts too :excited:

doug sinclair
12-07-2013, 10:14 AM
I wonder how long it will be before we have another AUGUST like the August in 2014. Perhaps that is what the supposed phenomenon might refer to! But I hear what you are saying. Any 31-day month that starts on a Saturday would have 5 of each.

Robert Gary
12-07-2013, 10:14 AM
Many of the wives of the guys in the chapters I attend are convinced simply because of the time and money we put into timepieces, we are all nuts!Nutjob

One of the presentations at the Ward Francillon Time Symposium this year in Pasadena, by E.C. Krupp, Director of the Griffith Observatory, was on the history and use of calendars over the history of mankind. If you want information on calendars of all types, that would be the lecture to obtain from the NAWCC library.

RobertG

RL
12-12-2013, 10:32 AM
Doug,
It has to start on a Friday.

Tom McIntyre
12-12-2013, 07:03 PM
Doug,
It has to start on a Friday.

:) Unless you are really interested in Saturday,Sunday and Monday.

I wonder what the most numerous Friday, Saturday, Sunday in a given year would be, taking into account, Leap Year and the lack of one in the 400 year cycle. Since there are 7 31 day months, I would guess that there will only be one of any sequence in a given year except for the year following leap year, but that is likely an oversimplification. I don't have the energy to duplicate Marty's feat of computation. :o

RL
12-15-2013, 06:26 PM
Tom,
Me neither! The energy or the math skills---lol!

Tom McIntyre
12-15-2013, 10:50 PM
It might be doable without too much math.

Assume a non-leap year with February 1st as a Monday. March 1st is a Monday and there are 5 Mon, Tue, Wed sequences. April starts on Thursday, but only has 4 three day sequences. May has 31 days and starts on Saturday so the 5 sequences are Sat, Sun, Mon. June starts on Tuesday but has 30 days. July starts on Thursday, so the sequence is Thu, Fri, Sat. August starts on Sunday for Sun, Mon, Tue. September is 30 days starting on Monday. October starts on Wednesday so the sequence is Wed, Thu, Fri. November is 30 days starting on Saturday. December starts on Monday and therefore has the same sequence as March. January starts on Thursday and has the same sequence as July.

In a leap year, the only change is that March starts a day later than February but the rest of the sequences are the same. December will duplicate March and January will duplicate July. The century and 400 year modifications likewise have no impact.

The leap years do, of course, change the particular week days that appear in the 7 sets and therefore also the ones that appear twice. The set also changes each year because of the remainder day each year after dividing by 7.

This counting exercise has a different result if the start is January first. March and December are the same but no other months are.

January Monday, March Thursday, May Tuesday, July Sunday, August Wednesday, October Saturday, December Thursday.

A year with 29 days in February is moved back by one day for all months save January.

January Monday, March Friday, May Wednesday, July Monday, August Thursday, October Sunday, December Friday. That change makes January align with July and March/December still align, of course since the number of days between them does not change and is divisible by 7.

(If I got this wrong please post a correction.:))

Ralph B
12-19-2013, 12:45 AM
Just to add to this fascinating thread.....

In this part of the World we denote the date in ascending order of size, so the 11th of December, 2013, is written 11/12/13.

This will only happen again in the year 2113.

Correct ?

Tom McIntyre
12-19-2013, 01:21 AM
That particular sequence will not occur for another 100 years. The sequence form has been fairly common recently starting with 1/2/3 in 2003, and displaying a similar sequence each year up until this year. The generalized form will return in 2103 and run for 11 years again.

Of course one might object to dropping the common leading zeros. In that case only 10/11/12 and 11/12/13 are of the pattern.

dweiss17
12-19-2013, 12:01 PM
Doug:

If you bought the NAWCC Chapter 190 Calendar for 10 bucks...you could have seen that phenomenon.

We still have some on hand to sell.

Dan.