EKsK - Everything Killsushi Knows

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====== Doomsday Algorithm ======

Doomsday Algorithm was an innovation by John Conrad for quickly mentally calculating the day of the week (e.g., 2001-09-11 was a Monday). It does so by associating a specific day of the week with a given year and identifying days in each month that always fall on that day with a simple mnemonic system, and also teaches how to find that specific weekday in other years within a century and the day for a given century. That day, for whatever reason, is called the *doomsday*. 

It's a nifty parlor trick, a decent mental exercise, and takes about as much skill as learning to solve a Rubik's cube in under a minute. 

===== Monthly doomsdays =====
The monthly doomsdays (after February) are trivial to remember: they fall on the same day as the month's number. 

^ Even "doomsdays" ^^
^ Month ^ Day ^
| April | 4 |
| June | 6 |
| August | 8 |
| October | 10 |
| December | 12 |

Odd doomsdays (after March) have a dumb mnemonic, "I work 9-5 at the 7/11" : 

^ Odd "doomsdays" ^^
^ Month ^ Day ^
| May | 9 |
| July | 11 |
| September | 5 |
| November | 7 |

March is an odd case: its doomsday is the 0th, or the last day of February. (so it's also March 7th, 14th, etc)

Depending on whether a year is a leap year or not, the Doomsday is likewise the 28th or 29th of February. 

The trick for figuring out January's doomsday is easy: 3/4ths of the time, a year isn't a leap year, so the doomsday is January 3rd. That 4th time, when a leap year occurs, it's January 4th. So, to summarize: 

^ Month ^ Doomsday ^
| January | 3 / 4 |
| February | 28 / 29 |
| March | 7 |
| April | 4 | 
| May | 9 |
| June | 6 |
| July | 11 |
| September | 5 |
| October | 10 |
| November | 7 |
| December | 12 | 

Not all of our brains are used to working with modulo seven, so here's an expanded table that can be memorized or used to learn the modulo seven operation. This is just for regular years. You can make your own chart for handling leap years. 

^ Months ^ Days ^
| February, March, November | 0, 7, 14, 21, 28 |
| August | 1, 8, 15, 22, 29 |
| May | 2, 9, 16, 23, 30 |
| January, October | 3, 10, 17, 24, 31 |
| April, July | 4, 11, 18, 25 |
| September, December | 5, 12, 19, 26 |
| June | 6, 13, 20, 27 |

Can you figure out this year's doomsday if you know the current date and day of the week? Try calculating other dates this year and consult a calendar to see whether it works out. 

===== Yearly doomsdays =====
Given the last exercise, with enough practice, calculating days of the week should be fairly trivial after you learn a year's doomsday. But what about doomsdays for other years? A simple algorithm was developed for this. The century doomsday of this century is **Tuesday** . This algorithm is based around the decade and digit years, eg for dates 2000 - 2099:

  - Is the current 2 digit year odd? If so, add 11. 
  - Divide it by 2. 
  - Is the current 2 digit year odd? If so, add 11. 
  - Count how many days it is from your new number to a multiple of 7. 

In case you're rusty on your 7s tables, the multiples of 7 are: 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105. Let's look at 2 examples of this algorithm in practice: 

23: 
  - is odd, add 11. -> 34
  - divide by 2 -> 17
  - is odd, add 11. -> 28
  - 0 days until a multiple of 7 (28)

That means 2023 has the same doomsday as the century year, Tuesday. Let's try another:

36:
  - isn't odd -> 36
  - divide by 2 -> 18
  - isn't odd -> 18
  - 3 days until a multiple of 7 (21)

Tuesday + 3 = Friday. Lo and behold, Friday is the doomsday of 2036. 

{{tag>math wip}}