DOOMSDAY Logs
2023 → Tuesday.
Century anchor for the 2000s = Tuesday (2). YY = 23:
q = 23 ÷ 12 = 1
r = 23 − 12 = 11
s = 11 ÷ 4 = 2
Sum: 2 + 1 + 11 + 2 = 16, mod 7 = 2 = Tuesday.
Check: 2023's doomsday is Tuesday. ✓ (4/4/2023 was a Tuesday.)
Q Why does the "q + r + s" sum give the year's doomsday drift?
Each common year moves the doomsday +1 and each leap year +2, so the drift is YY + (leap years) = YY + YY÷4 — and the 12-split is just an easy way to compute that mod 7.
A normal year is 365 = 52·7 + 1 days, so the calendar shifts one weekday; a leap year shifts two. Over YY year...
Q There's an alternative year method, "odd + 11." When might you use it?
It's another route to the same year's doomsday; use whichever feels faster — both give identical results.
The "odd + 11" method: if YY is odd add 11, halve it, if that's odd add 11 again, take mod 7, and subtract from 7. It reaches the same answer as the 12-remainder-quarter meth...
Q What are the century anchor days you need to memorise?
A doomsday for each century's "00" year: 1800s → Friday, 1900s → Wednesday, 2000s → Tuesday, 2100s → Sunday.
Century
Anchor
#
1700s / 2100s
Sunday
0
1800s / 2200s
Friday
5
1900s / 2300s
Wednesday
3
2000s / 1600s
Tuesday
2
The pattern repeats every 400 years (the G...
Q What are quick memory hooks for the two most-used century anchors?
2000s = Tuesday ("Y2K → Twos-day"); 1900s = Wednesday.
2000s → Tuesday: the year 2000 doomsday was a Tuesday — think "Y2K, Twosday" (2 = Tuesday's number).
1900s → Wednesday: the workhorse anchor for 20th-century dates.
From those two you can reach the others via the 400-year c...
Q How do you turn the century anchor into the year's doomsday (the "12-remainder-quarter" method)?
Split the last two digits with 12: doomsday = anchor + q + r + s (mod 7), where q = YY÷12, r = the remainder, s = r÷4.
For year 19YY:
q = how many whole 12s in YY.
r = what's left over (YY − 12q).
s = r ÷ 4 (whole part).
Add q + r + s to the century anchor, mod 7.
This small su...
Q Work out the doomsday for 1978 step by step.
1978 → Tuesday.
Century anchor for the 1900s = Wednesday (3). Now YY = 78:
q = 78 ÷ 12 = 6
r = 78 − 72 = 6
s = 6 ÷ 4 = 1
Sum: 3 + 6 + 6 + 1 = 16, and 16 mod 7 = 2 = Tuesday.
Check: 1978's doomsday is indeed Tuesday. ✓ (So 4/4/1978, 6/6/1978, etc. were all Tuesdays.)
Q What is the leap-year rule you must apply?
A year is a leap year if it's divisible by 4 — except century years, which must be divisible by 400.
2020 → ÷4 → leap. ✓
1900 → ÷100 but not ÷400 → not leap.
2000 → ÷400 → leap. ✓
2023 → not ÷4 → not leap.
This matters because leap years change the January and February doomsday...
Q What are the doomsday dates for January and February — and why do they depend on the year?
February's doomsday is the last day of February (2/28, or 2/29 in a leap year); January's is the 3rd, bumping to the 4th in a leap year. Both land on the same weekday, so they move together.
February: the last day — 2/28, or 2/29 in a leap year. It is the leap boundary, so there...
Q What are the three steps of the Doomsday method?
Century anchor → year's doomsday → count from the nearest doomsday date to your target.
Century anchor — a memorised weekday for the century (2000s → Tuesday, 1900s → Wednesday).
Year's doomsday — adjust the anchor by a small calculation on the last two digits of the year.
The d...