What day of the week is March 1, 2017? November 15, 2017? August 22, 2017?
2017 is a very special year – it makes day of week calculations easy-peasy, and opens the door for doing it for any day – any year – or any century.
Tempted to try? Then just look at this list of 12 numbers:
6 2 2 5 0 3 5 1 4 6 2 4
Let’s put them in context:
How it works: Each number after January’s is the offset in the calendar for the next month, modulo 7 (or, wrapping around weekly, where 6 is Saturday, and 7 becomes 0, which is Sunday, then 1 for Monday, etc.) Take June (3) which is 30 days, or 7+7+7+7+2 – the 7s don’t count (Wednesday plus 7 days is still Wednesday – get it?) However the 2 does count, so the number for July is the 3 for June plus the extra 2 days, or 5. And as January shows, you wrap around from 6 to 0 – January has an extra 3 days, and 6+3=9, which you fix by subtracting 7, to get 2. Using this and the number 6, we can create this whole list ourselves, but it pays to memorize it. Note we also use the ‘normal’ February, which is 28 days, no no extra to add to March, so it remains 2 as well.
And 2017 is special because the year started at 0 (Sunday.) Put that together and we have very simple calculations by adding this ‘Month Number’ and the date of the month:
- January 1, 2017? January is 6, plus 1 for the first is 7. subtract 7 (days always run from 0=Sunday to 6=Saturday) and we get 0, or Sunday.
- March 1, 2017? March=2 + 1st=3, which is Wednesday.
- November 15, 2017? November=2; 2+15=17; keep removing 7s until we get 3, which is Wednesday again.
- August 22, 2017? August=1; 1+22=23, which is 7+7+7+2; throw away the 7s, and we get 2, or Tuesday.
What makes the calculation so simple is that 2017 starts on a Sunday, so very little math is needed – add the Month number and Month’s date, and throw out the sevens to get a day. It also works for any non-leap year year that starts on a Sunday, such as 2023 and 2034.
Of course, once you’ve had some practice, you probably don’t want a trick you get to use only one or twice a decade. So how to expand on this to get the day of the week for any date? Tune in to tommorrow’s part 2 for more…