Calendar guide or educational program for not very advanced
“In July 2011, 5 Fridays, 5 Saturdays, 5 Sundays. This happens once in 823 years "
Surely, you have often met such "revelations" on the Internet, primarily on Twitter. A couple of times a year, the flood necessarily begins on the subject of how rare this event is - 5 Fridays, Saturdays and Sundays in one month.
The reason for this joy is perfectly understandable - after all, it turns out that this month there are more than usual weekends and days when it is customary to get drunk! It’s just a lagging realization that this doesn’t make such days a year anymore.
But I am outraged not by flood and unreasonable joy, but by the stupidity of the statement that this is such a rare event that it happens once in 823 years. Everyone repeats it one after another like parrots, without even thinking about the correctness of this statement. In the meantime, this is a frank nonsense, because such months often fall out, much more often than the short-minded “experts” of the calendar say.
')
The last time that such an event happened, I took out my anger and rage against one decent person, with whom I no longer communicate as a result. But henceforth I decided not to repeat this error, but to write a small article on educational information, to which I will now send all parrots.
For a start, let's consider what a special month is, in which there are 5 Fridays, Saturdays and Sundays. For example, let's take the same July 2011:
As it is easy to see, 5 Fridays, Saturdays and Sundays in one month (we will call such months “magic”) can only be if two conditions are met:
There are seven months out of 31 days in the calendar: January, March, May, July, August, October, December. Months starting on Friday are also not uncommon, which is obvious. Such were, for example, October 2010, January 2010, etc.
Moreover, the day from which one or another month begins depends only on which day of the week the year begins and whether this year is a leap year (for all months except January). For each pair of "year / leap year - month" offset by the difference in days of the week is constant. See the table:
Actually, this shift accumulates with each month and is equal to the remainder of the division by 7 the number of days in each month (January - 3, February - 0 or 1, March - 3, etc.). That is, the offset is 3 days for each month of 31 days, 2 days for months of 30 days and 0/1 day for February, which is so special for us (1 for a leap year).
Note that the offset is displayed as the remainder of dividing by 7 (that is, we have a ring of residue classes modulo seven ).
Table number 1.
Please note that according to the results of the year, the total offset will be 1 for the regular year and 2 for the leap year, which is completely true - the remainder of dividing 365 by 7 is 1, and the remainder of dividing is 366-2.
So, we have the result that we want to get - we need the month to start on Friday. We know the shift from the beginning of the year, so it is easy to determine from which day the year should begin for each of the months in order for this month to become "magical."
The following table follows from the previous one (here we are only interested in only 7 months). That is, for each month we get the day of the week, from which the year must begin in order for this month to be “magic”:
Table number 2.
You can see that this year started on Saturday and is not a leap year, so July became “magical”.
It turns out that such months are in almost every year:
Table number 3.
It turns out that “magical” months are not such a rarity. It happens even for two such months in one year. Although sometimes it happens that for the whole year there is not one such month.
Consider now the thesis that the "magic" July happens every 823 years. As we have already shown, this July happens every non-leap year that begins on Saturday. Is it really such a rarity - the year starting on Saturday? Common sense tells us that this is a common thing, and given the shift to 1 day of the week each year (and 2 each leap year), this should happen about once every 7 years.
We will not consider all past and future years, just take a look at the years from 2000 to 2022 (see below why these are exactly):
Table number 4.
Thus, the years 2000, 2005, 2011 and 2022 begin on Saturday, but 2000 is a leap year, therefore it does not suit us. But even so, in about 20 years a “magical” July occurs three times . You can see for yourself by looking at the calendar.
So, you can now easily "predict" what the magic months will soon be. And do not write, please, nonsense about the fact that this happens every 823 years. And don't retweet!
Surely, you have often met such "revelations" on the Internet, primarily on Twitter. A couple of times a year, the flood necessarily begins on the subject of how rare this event is - 5 Fridays, Saturdays and Sundays in one month.
The reason for this joy is perfectly understandable - after all, it turns out that this month there are more than usual weekends and days when it is customary to get drunk! It’s just a lagging realization that this doesn’t make such days a year anymore.
But I am outraged not by flood and unreasonable joy, but by the stupidity of the statement that this is such a rare event that it happens once in 823 years. Everyone repeats it one after another like parrots, without even thinking about the correctness of this statement. In the meantime, this is a frank nonsense, because such months often fall out, much more often than the short-minded “experts” of the calendar say.
')
The last time that such an event happened, I took out my anger and rage against one decent person, with whom I no longer communicate as a result. But henceforth I decided not to repeat this error, but to write a small article on educational information, to which I will now send all parrots.
Coordinates of wonders
For a start, let's consider what a special month is, in which there are 5 Fridays, Saturdays and Sundays. For example, let's take the same July 2011:
As it is easy to see, 5 Fridays, Saturdays and Sundays in one month (we will call such months “magic”) can only be if two conditions are met:
- The month should consist of 31 days.
- The month should start on Friday.
There are seven months out of 31 days in the calendar: January, March, May, July, August, October, December. Months starting on Friday are also not uncommon, which is obvious. Such were, for example, October 2010, January 2010, etc.
Digging deeper
Moreover, the day from which one or another month begins depends only on which day of the week the year begins and whether this year is a leap year (for all months except January). For each pair of "year / leap year - month" offset by the difference in days of the week is constant. See the table:
Actually, this shift accumulates with each month and is equal to the remainder of the division by 7 the number of days in each month (January - 3, February - 0 or 1, March - 3, etc.). That is, the offset is 3 days for each month of 31 days, 2 days for months of 30 days and 0/1 day for February, which is so special for us (1 for a leap year).
Note that the offset is displayed as the remainder of dividing by 7 (that is, we have a ring of residue classes modulo seven ).
Table number 1.
| Month | Monthly bias | Monthly displacement | Offset with the beginning of the year | Offset with the beginning of the year (hs.) |
|---|---|---|---|---|
| January | 3 | 3 | 0 | 0 |
| February | 0 | one | 3 | 3 |
| March | 3 | 3 | 3 | four |
| April | 2 | 2 | 6 | 0 |
| May | 3 | 3 | one | 2 |
| June | 2 | 2 | four | five |
| July | 3 | 3 | 6 | 0 |
| August | 3 | 3 | 2 | 3 |
| September | 2 | 2 | five | 6 |
| October | 3 | 3 | 0 | one |
| November | 2 | 2 | 3 | four |
| December | 3 | 3 | five | 6 |
Please note that according to the results of the year, the total offset will be 1 for the regular year and 2 for the leap year, which is completely true - the remainder of dividing 365 by 7 is 1, and the remainder of dividing is 366-2.
Removing the truth to the light
So, we have the result that we want to get - we need the month to start on Friday. We know the shift from the beginning of the year, so it is easy to determine from which day the year should begin for each of the months in order for this month to become "magical."
The following table follows from the previous one (here we are only interested in only 7 months). That is, for each month we get the day of the week, from which the year must begin in order for this month to be “magic”:
Table number 2.
| Month | Sought for beginning of the year | Sought for beginning of the year (hs.) |
|---|---|---|
| January | Friday | Friday |
| March | Tuesday | Monday |
| May | Thursday | Tuesday |
| July | Saturday | Friday |
| August | Wednesday | Tuesday |
| October | Friday | Thursday |
| December | Sunday | Saturday |
You can see that this year started on Saturday and is not a leap year, so July became “magical”.
It turns out that such months are in almost every year:
Table number 3.
| Beginning of the year | "Magic" months | "Magic" months (vis.) |
|---|---|---|
| Monday | - | March |
| Tuesday | March | May, August |
| Wednesday | August | - |
| Thursday | May | October |
| Friday | January, October | January, July |
| Saturday | July | December |
| Sunday | December | - |
It turns out that “magical” months are not such a rarity. It happens even for two such months in one year. Although sometimes it happens that for the whole year there is not one such month.
Once in 823 years
Consider now the thesis that the "magic" July happens every 823 years. As we have already shown, this July happens every non-leap year that begins on Saturday. Is it really such a rarity - the year starting on Saturday? Common sense tells us that this is a common thing, and given the shift to 1 day of the week each year (and 2 each leap year), this should happen about once every 7 years.
We will not consider all past and future years, just take a look at the years from 2000 to 2022 (see below why these are exactly):
Table number 4.
| Year | Start | Bias |
|---|---|---|
| 2000 (hight) | Saturday | 2 |
| 2001 | Monday | one |
| 2002 | Tuesday | one |
| 2003 | Wednesday | one |
| 2004 (vis) | Thursday | 2 |
| 2005 | Saturday | one |
| 2006 | Sunday | one |
| 2007 | Monday | one |
| 2008 (hung) | Tuesday | 2 |
| 2009 | Thursday | one |
| 2010 | Friday | one |
| 2011 | Saturday | one |
| 2012 (hung) | Sunday | 2 |
| 2013 | Tuesday | one |
| 2014 | Wednesday | one |
| 2015 | Thursday | one |
| 2016 (hung) | Friday | 2 |
| 2017 | Sunday | one |
| 2018 | Monday | one |
| 2019 | Tuesday | one |
| 2020 (hight) | Wednesday | 2 |
| 2021 | Friday | one |
| 2022 | Saturday | one |
Thus, the years 2000, 2005, 2011 and 2022 begin on Saturday, but 2000 is a leap year, therefore it does not suit us. But even so, in about 20 years a “magical” July occurs three times . You can see for yourself by looking at the calendar.
So, you can now easily "predict" what the magic months will soon be. And do not write, please, nonsense about the fact that this happens every 823 years. And don't retweet!
Source: https://habr.com/ru/post/120870/
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