Weekday numbers

Weekday numbers

In order to do simple arithmetic operations on dates, we must think of the days of the week not as names but as numbers.

It is the smallest piece of memorisation in the whole method — seven numbers — and every later step leans on it.

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 a few useful mnemonics to help you memorise these weekday numbers:

Once the days are numbers, questions about the calendar turn into small additions: a weekday plus a count of days.

Speed in this algorithm depends on your comfort with mental calculations like Tuesday (2) plus 2 equals Thursday (4). A trickier example is Saturday (6) plus 6 equals Friday (5), which may seem counterintuitive since 6 + 6 equals 12, not 5. This is where the modulo operation comes in.

Modulo is just the remainder after a division. Add your days, divide the total by 7, and the remainder is the weekday number — every 7 days, the week is back where it started.

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.

That wrap-around is the only arithmetic trick the method uses. Everything from here on is the same move again — add small numbers, throw away the sevens.