Doomsday Trainer

Conway's Doomsday method gives the weekday of any date without a calendar. Every year has a doomsday: one weekday shared by 4/4, 6/6, 8/8, 10/10, 12/12 and a few other easy dates. Find the year's doomsday, then count from the nearest one.

All weekday arithmetic uses these numbers: Sunday is 0 and Saturday is 6, and everything wraps at 7. On the trainers, keys 0 to 6 pick an answer and Enter moves to the next question.

1. 1

   Century anchor

   Take the first two digits of the year as the century number c, so 2026 gives c = 20. Divide c by 4 and keep the remainder. The pattern repeats every 400 years.

   Check formula: anchor = (5 × remainder + 2) mod 7.

   Drill step 1
2. 2

   Year doomsday

   Take the last two digits, y. Count the twelves in y (a), the leftover (b), and the fours in the leftover (c). Add them, wrap at 7, then add the result to the anchor.

   offset = (a + b + c) mod 7 year doomsday = anchor + offset

   Example, 1987: 87 is 7 twelves with 3 left over, and 3 holds no fours. 7 + 3 + 0 = 10, which wraps to 3. The 1900s anchor is Wednesday, and Wednesday + 3 is Saturday.

   Drill step 2
3. 3

   Month doomsday

   Every month has one easy date that always lands on the year's doomsday weekday.

   Even months repeat their number: 4/4, 6/6, 8/8, 10/10, 12/12. The odd pairs are 5/9, 9/5, 7/11 and 11/7, the 9-to-5 at the 7-Eleven. March 14 is Pi Day. January and February use 3 and 28, which become 4 and 29 in a leap year.

   Leap years are divisible by 4, except century years not divisible by 400. So 1900 and 2100 are not leap years, and 2000 is.

   Drill step 3
4. 4

   Count from the nearest doomsday

   Dates 7 days apart share a weekday, so every 7th day from the month's doomsday date is also a doomsday. Find the one closest to your date, count the gap, and move that many weekdays.

   Example, October 7, 2026: the year's doomsday is Saturday, so October 3, 10, 17, 24 and 31 are Saturdays. The 7th is 3 days before the 10th, and Saturday minus 3 is Wednesday.

   Drill step 4

Walk through any date

Step 1: Century anchor

The anchor repeats every 400 years, so only four values matter. Divide the century number by 4 and read the remainder.

Step 2: Year doomsday

Split the last two digits into twelves, then the leftover into fours. Add the twelves, the leftover and the fours, and wrap at 7.

Offset mode drills the arithmetic on its own. Full year doomsday mode also needs the century anchor from step 1.

Step 3: Month doomsdays

Learn these twelve dates cold. The only variable is leap year, which moves January and February. Months you miss come up more often.

Step 4: Count from the doomsday

You are given the year's doomsday. List the month's doomsday dates (every 7 days from the one you know), pick the nearest, and count the gap.

Final trainer

Random dates, all four steps. Answer with the weekday, and a full breakdown of that exact date opens after every answer, right or wrong. Aim to get faster without losing accuracy.