The Doomsday Algorithm

Mental Math · Axiom Academy

Master John Conway's ingenious method for mentally calculating the day of the week for any date What is a Doomsday? In Conway's system, the "doomsday" is a specific day of the week that certain memorable dates always fall on within a given year. These dates are carefully chosen to be easy to remember and evenly distributed throughout the year. 5/9 (May 9th) - "9 to 5 at the 7-11" All of these dates fall on the same day of the week in any given year! This day is called the "doomsday" for that year. 2. Finding the Century's Anchor Day The first step in calculating a date's day of the week is determining the "anchor day" for the century. The anchor day is the doomsday for years ending in 00 (like 1900, 2000, 2100). The pattern repeats every 400 years, so 2400s will be Tuesday again (like the 2000s). 3. Calculating the Year's Doomsday Now we need to find the doomsday for the specific year. This involves a simple calculation using the last two digits of the year. Take the last two digits of the year (YY) Divide YY by 12, note the quotient (a) Divide the remainder by 4, note the quotient (c) Reduce modulo 7 to get the day of week Once you know the year's doomsday, you can find any date by counting days from the nearest doomsday. January: 1/3 (or 1/4 in leap years) February: 2/28 (or 2/29 in leap years) - "Last day of February" March: 3/0 (think of it as 2/28 or 2/29) April-December: Use the memorable dates from Step 1

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