๐Ÿ—“๏ธ Weekday Trick

Work out the day of the week for any date โ€” in your head.

Pick any date to see the trick worked out, step by step

 

What day of the week was this?

 

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Doomsday dates: 4/4, 6/6, 8/8, 10/10, 12/12, and "9-to-5 at 7-Eleven" โ€” 9/5, 5/9, 7/11, 11/7. Plus 3/14 (Pi Day), and 3 Jan / 28 Feb, which become 4 Jan / 29 Feb in a leap year.

Century anchors: 1600s and 2000s Tuesday ยท 1700s and 2100s Sunday ยท 1800s and 2200s Friday ยท 1900s and 2300s Wednesday.

Year: take the last two digits, add the whole 12s, the leftover, and the leap years inside the leftover.

How the trick works

Every year has one weekday โ€” its doomsday โ€” that a handful of easy dates all land on. Learn those dates, work out the doomsday for the year, and then count a few days forward or back.

1๏ธโƒฃ Memorize the doomsday dates

These fall on the same weekday in any given year. The even months pair with themselves; the odd ones are the "9-to-5 at 7-Eleven" pairs:

4/4   6/6   8/8   10/10   12/12   and   9/5   5/9   7/11   11/7

March is 3/14, Pi Day. January and February are the odd ones out: 3 January and 28 February normally, but 4 January and 29 February in a leap year โ€” so the last day of February is always a doomsday.

2๏ธโƒฃ Learn the four century anchors

The pattern repeats every 400 years, so four weekdays cover every century:

1600s, 2000s, 2400sTuesday
1700s, 2100sSunday
1800s, 2200sFriday
1900s, 2300sWednesday

If you'd rather compute it than remember it: (5 ร— (century mod 4) + 2) mod 7, counting Sunday as 0.

3๏ธโƒฃ Step from the anchor to the year

Take the last two digits of the year, then add three numbers to the anchor: how many whole 12s fit, what's left over, and how many leap years hide in that leftover.

1987 โ†’ 87 = 7ร—12 + 3, and 3 รท 4 = 0 โ†’ 7 + 3 + 0 = 10

The 1900s anchor is Wednesday, and 10 days past Wednesday is Saturday. So every doomsday date in 1987 โ€” 4 April, 6 June, 9 May โ€” is a Saturday.

โž— Another way to do step 3: odd + 11

Same result, different arithmetic โ€” two halvings instead of three additions. Some people are faster this way; try both and keep the one your head likes.

Take the last two digits, then: if it's odd, add 11. Halve it. If that's odd, add 11. Finally subtract what's left over from the next multiple of 7.

87 โ†’ +11 = 98 โ†’ รท2 = 49 โ†’ +11 = 60 โ†’ 7 โˆ’ (60 mod 7) = 3

Wednesday + 3 is Saturday โ€” the same 1987 doomsday the 12s method found. The two offsets, 10 and 3, differ by exactly a week, so they always land on the same day. Learn mode shows both rows side by side for whatever date you pick.

4๏ธโƒฃ Count to your date

Find the doomsday date in the same month and count the difference, dropping whole weeks as you go.

12 June 1987: 6 June is a Saturday, +6 days โ†’ Friday

๐Ÿ•ฐ๏ธ One caveat about old dates

This is the Gregorian calendar, and countries adopted it at different times โ€” Britain in 1752, Sweden in 1753. For a date before then, the answer is what the Gregorian calendar would have said, not what the almanac of the day printed.