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Ready-reference calendar.
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Previously:
https://www.homemadetools.net/forum/...555#post197268
https://www.homemadetools.net/forum/...340#post116509
https://www.homemadetools.net/forum/...938#post119860
Or, one can learn the doomsday algorithm...
The so-called doomsday algorithm is a neat trick that will allow you to mentally work out the day-of-the-week (DOW) for any date. It's amazing how frequently this trick will come in handy.
Doomsday is, by definition, the DOW of the last day of February (2/28 or 2/29 in a leap year).
Aside: In Roman times, the year started on March first. The Romans sensibly added the leap day at the end of the year, which would have been the day before March first. As months were added and manipulated, this detail was retained and that's why our leap day is at the end of February rather than the end of December where it belongs.
The algorithm is based on two observations:
For months 4,6,8,10,12, the dates 4/4, 6/6, 8/8, 10/10, and 12/12 the DOW is the same as the doomsday DOW.
Memorize the mnemonic, "I work from 9 to 5 in the 7-11". (For non-US readers, '7-11' is the name of a chain of popular convenience stores in the USA, presumably named for the hours when they are open for business.)
Observe that the dates 5/9, 9/5, 7/11 and 11/7 also fall on the doomsday DOW.
So, if I know the doomsday for the current year, I can quickly work out the DOW for any date in that year.
An example will help. The doomsday for 2021 (the year of this writing) is Sunday. On what DOW will Christmas fall this year? From the algorithm, we know that 12/12 is a Sunday. So, adding two weeks (14 days), we know that 12/26 is a Sunday. Therefore, Christmas must fall on a Saturday.
Observant readers will notice that I haven't addressed the first three months of the year. The last day of February (2/28 or 2/29 in a leap year) is *always* a doomsday. Therefore the first day of March is always the day after doomsday. If the last day of February is the 28th then 2/28 - 28 = 2/0 = 1/31 is a doomsday. If the last day of February is the 29th then 2/29 - 28 = 2/1 is a doomsday and 1/31 is the day before doomsday.
So, the algorithm allows you to mentally establish the DOW for a specific date in each month. From that, it's a simple matter of doing some modulo seven arithmetic to get to whichever date is of interest - as I did in the Christmas example above.
The procedure then becomes one of memorizing the DOW for the last day of February at the start of the year. From that knowledge and the algorithm above, finding the DOW for any other date in the year is straightforward.
Now all we need is a means of calculating doomsday for any year.
There are algorithms for calculating the doomsday for any year. However, in the interest of simplicity, I'll only present a simpler version that will allow calculating doomsday for years in the most relevant interval 1900 to 2099...
Express the year in the form:
Year = AABB, AA=19 or 20
than the DOW of doomsday is given by:
Doomsday = {BB + [BB/4] + (22-AA)} mod 7
This equation will produce a DOW integer between zero and six with zero denoting Sunday and six denoting Saturday.
Example:
Year = 2021, AA=20, BB=21
[22/4] = 5
{21 + 5 + (22-20)} mod 7 = 28 mod 7 = 0 = Sunday
The bracket notation (i.e. [22/4]) denotes integer division, making the indicated division and retaining only the integer part of the quotient.
The mod (short for modulo) indicates making the indicated division and retaining only the remainder, e.g. 111 mod 5 = 1, 111 = 22*5 with a remainder of 1.
Most Usonians will remember the DOW of Pearl Harbor (12/7/1941). As an example, Let's verify the algorithm...
{41 + 10 + 3} mod 7 = 54 mod 7 = 5 = Friday = doomsday DOW for 1941
12/12 was a Friday so 12/5 was a Friday so 12/7 was a Sunday which is indeed correct.
I put a thanks to mklotz's eloquent and interesting explanation, not that I would remember it longer than it took me to read it though.
However for an expanded version I direct us to
http://www.rudy.ca/doomsday.html
My explanation is a lot to read but there isn't much one must remember to use the algorithm.
DOW for last day in February = DD (Doomsday)
4/4, 6/6, 8/8, 10/10, and 12/12 are DD
I work from 9 to 5 in the 7-11
5/9, 9/5, 7/11 and 11/7 are DD
3/14 (pi day) is always a DD
1/3 is DD three years out of four, the non-leap years. It's 1/4 only in the fourth year, the leap years divisible by 4.