# Doomsday Algorithm

## Use the simplified Doomsday Algorithm to find the day name of any date this century.

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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.

 1 What day of the week is28th November 2018? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗ 2 What day of the week is20th August 2054? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗ 3 What day of the week is26th July 2049? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗ 4 What day of the week is7th October 2046? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗ 5 What day of the week is11th April 2084? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗ 6 What day of the week is25th March 2035? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗ 7 What day of the week is2nd March 2016? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗ 8 What day of the week is10th November 2036? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗ 9 What day of the week is10th March 2089? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗ 10 What day of the week is23rd October 2056? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗ 11 What day of the week is8th October 2014? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗ 12 What day of the week is7th August 2024? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗ 13 What day of the week is25th October 2091? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗ 14 What day of the week is19th May 2080? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗ 15 What day of the week is9th December 2011? ☐ Which Day? Monday Tuesday Wednesday Thursday Friday Saturday Sunday ☐ ✓ ✗
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This is Doomsday Algorithm level 4. You can also try:
Level 1 Level 2 Level 3

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## Description of Levels

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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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## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

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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