In order to do simple arithmetic operations on dates, we must think of the days of the week not as names but as numbers.
Luckily, this is very easy to learn and to remember.
In the doomsday algorithm, each weekday has a number, starting with Sunday as 0 and Monday as 1, up to Saturday as 6. There are some useful mnemonics that we can use to help us memorising these weekday numbers:
The foundational arithmetic skill in the Doomsday algorithm involves adding and subtracting numbers from a weekday. This skill is essential for swiftly calculating the correct weekday, and it requires a comfortable familiarity with the concept that days of the week are represented as numbers.
Speed in this algorithm depends on your comfort with mental calculations like Tuesday (2) plus two equals Thursday (4). A trickier example is Saturday (6) plus 6 equals Friday (5). It may seem counterintuitive since 6 + 6 equals 12, not 5. This is where understanding the modulo operation becomes crucial.
The modulo can be understood as a way to find the remainder of a division. In the context of the doomsday rule, when you add days to a date, you divide the total number of days by 7 (since there are 7 days in a week) and the remainder gives you the correct weekday.
For example, in the case of Saturday (6) plus 6, you calculate 6 + 6 = 12. Now, divide 12 by 7. The quotient is 1 (which represents one complete week) and the remainder is 5. Thus, 12 modulo 7 is 5, which corresponds to Friday. So, Saturday plus 6 days indeed lands on a Friday.
This modulo operation ensures that no matter how many days you add, you’ll always land on a valid day of the week. It’s like a clock that wraps around after reaching the highest number — in this case, Saturday (6).
Here’s another example: If it’s Wednesday (3) and you want to find the day 10 days later, you calculate 3 + 10 = 13. Performing the modulo operation, 13 modulo 7 is 6, which is Saturday.
Therefore, the key to mastering the doomsday algorithm lies in getting comfortable with quickly performing these modulo operations. The more you practice, the easier it becomes to instantly know the day of the week for any given date.