Doomsday Algorithm

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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.

Step 1:

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 $

Step 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.

Step 3:

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.

Step 4:

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.

Step 5:

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.

What day of the week is
26th July 2092?

☐ ☐ ✓ ✗

What day of the week is
21st February 2023?

☐ ☐ ✓ ✗

What day of the week is
21st September 2063?

☐ ☐ ✓ ✗

What day of the week is
16th August 2080?

☐ ☐ ✓ ✗

What day of the week is
4th April 2092?

☐ ☐ ✓ ✗

What day of the week is
15th December 2039?

☐ ☐ ✓ ✗

What day of the week is
15th March 2035?

☐ ☐ ✓ ✗

What day of the week is
21st September 2005?

☐ ☐ ✓ ✗

What day of the week is
10th October 2098?

☐ ☐ ✓ ✗

What day of the week is
12th November 2061?

☐ ☐ ✓ ✗

What day of the week is
20th September 2079?

☐ ☐ ✓ ✗

What day of the week is
13th March 2064?

☐ ☐ ✓ ✗

What day of the week is
10th February 2079?

☐ ☐ ✓ ✗

What day of the week is
13th February 2073?

☐ ☐ ✓ ✗

What day of the week is
21st May 2072?

☐ ☐ ✓ ✗

Check

This is Doomsday Algorithm level 4. You can also try:
Level 1 Level 2 Level 3

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