Doomsday AlgorithmUse the simplified Doomsday Algorithm to find the day name of any date this century. 
This is level 4: John Conway's Method for dates this century. You will be awarded a trophy if you get at least 12 answers correct and you do this activity online.
Find what day number New Year's Day (NYD) was of the year in question using this formula:
$$ NYD = (YY  1 + YY\div4 \text{(rounded up)}) \text{ MOD } 7 $$where \(YY\) are the last two digits of the year and "MOD 7" means the remainder when divided by seven.
For example let's take the year 2019. The New Year's Day Number is:
\( NYD = (19  1 + 19\div4 \text{(rounded up)}) \text{ MOD } 7 \\ NYD = (19  1 + 5 ) \text{ MOD } 7 \\ NYD = (23) \text{ MOD } 7 = 2 \)
Add 2 to this number (or 3 if it's a leap year) then look up the day name in this table.
Sunday  0 
Monday  1 
Tuesday  2 
Wednesday  3 
Thursday  4 
Friday  5 
Saturday  6 
For example for the year 2019, we have that new years day is 2 so adding two to that (as 2019 is not a leap year because 19 is not exactly divisible by four) gives 4.
As can be seen from the table a 4 is Thursday.
The day name you now have is called the Doomsday for the year in question.
There is a Doomsday on the same day of the week for each month as shown in the following table (with hints I use to remember them):
January  3rd (4th leap year)  
February  28th (29th leap year)  Last day 
March  14 / 3  Pi Day 
April  4 / 4  
May  9 / 5  Nine to five 
June  6 / 6  
July  11 / 7  Not Seven Eleven 
August  8 / 8  
September  5 / 9  Not Nine to five 
October  10 / 10  
November  7 / 11  Seven Eleven 
December  12 / 12 
So for 2019, the 'Doomsday' is a Thursday.
That means that all of the dates in the table above are also Thursdays.
Find the month in question in the table above and remember it's Doomsday
For example suppose we are trying to find the day of the week that 14th July 2019 fell on. This step requires you to realise from the table above that the 11th July was a Thursday.
Finally you should (if you know your 7 times table) be able to work out the day in question according to how far it is away from that month's Doomsday (that may require a little practice  which is provided below).
Now we know that that the 11th July was a Thursday we need to count on three days to get to the date we are interested in. Three days after Thursday is Sunday. Therefore the 14th July 2019 fell on a Sunday.
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❎Level 1  Finding days less than a week away
Level 2  Finding days in same month
Level 3  Finding days in different months
Level 4  John Conway's Method for dates this century
Birthdays  Happy Birthday Maths activities.
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The excellent video above describes John Conway's Doomsday Algorithm in great detail  far more detail than my simplified version. There is also an excellent video from Mind Your Decisions from which I have used the NYD formula.
Here is an example calculation based on the steps I have provided:
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