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
22nd September 2067?

☐ ☐ ✓ ✗

What day of the week is
7th May 2091?

☐ ☐ ✓ ✗

What day of the week is
24th October 2080?

☐ ☐ ✓ ✗

What day of the week is
12th December 2085?

☐ ☐ ✓ ✗

What day of the week is
9th November 2069?

☐ ☐ ✓ ✗

What day of the week is
7th November 2040?

☐ ☐ ✓ ✗

What day of the week is
26th August 2059?

☐ ☐ ✓ ✗

What day of the week is
18th April 2098?

☐ ☐ ✓ ✗

What day of the week is
2nd December 2026?

☐ ☐ ✓ ✗

What day of the week is
24th November 2055?

☐ ☐ ✓ ✗

What day of the week is
17th February 2075?

☐ ☐ ✓ ✗

What day of the week is
13th September 2087?

☐ ☐ ✓ ✗

What day of the week is
13th May 2014?

☐ ☐ ✓ ✗

What day of the week is
26th April 2051?

☐ ☐ ✓ ✗

What day of the week is
9th October 2061?

☐ ☐ ✓ ✗

Check

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

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