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04 · All together
Full BDAY
Put the pieces together. Follow the fields at first; switch to mental mode when you want to work without intermediate answers.
How it works — step by step
Find the century anchor, reduce the last two year digits by 28/56/84, calculate the year anchor, then use the month’s reference date. Keep each result while you work on the next step.
25 December 1981: century 4 → 81 − 56 = 25 → 25 + 6 = 31 → remainder 3 → year anchor 7 → 25 − 12 = 13 → 7 + 13 = 20 → Friday = 6.
Century anchors · 1643
| Century year | Remainder ÷ 400 | Anchor |
|---|---|---|
| 1700 | 100 | 1 · Sunday |
| 1800 | 200 | 6 · Friday |
| 1900 | 300 | 4 · Wednesday |
| 2000 | 0 | 3 · Tuesday |
Why 28?
- Keep the last two digits: 1981 → 81.
- Subtract the largest of 84, 56 or 28 that fits. If the number is below 28, subtract 0. Here: 81 − 56 = 25.
- Divide the reduced number by 4 and keep only the whole part: 25 ÷ 4 → 6.
- Add: 25 + 6 = 31. Remove complete weeks: 31 − 28 = 3.
- Add the century anchor: 4 + 3 = 7. The year anchor for 1981 is Saturday.
In this year calculation, 28 years contribute 28 + 7 = 35 days, exactly five weeks. Subtracting 28, 56 or 84 from the last two digits therefore preserves the remainder. Apply this shortcut within the year’s last two digits; the century anchor handles century changes.
Month anchors
| Month | Common year | Leap year |
|---|---|---|
| January | 3 | 4 |
| February | 28 | 29 |
| March | 14 | 14 |
| April | 4 | 4 |
| May | 9 | 9 |
| June | 6 | 6 |
| July | 11 | 11 |
| August | 8 | 8 |
| September | 5 | 5 |
| October | 10 | 10 |
| November | 7 | 7 |
| December | 12 | 12 |
January and February change in leap years: 4 January and 29 February instead of 3 January and 28 February. A year is leap if divisible by 4, except century years unless also divisible by 400. So 1900 and 2100 are common years; 2000 is leap.
BDAY numbers the weekdays from Sunday = 1 to Saturday = 7. A remainder of 0 means Saturday when you turn a final weekday total into a day number.
Exercise
May 17, 1994
This session only. Each exercise counts once.
Gregorian calendar, years 1–9999. Earlier dates are calculated using Gregorian rules extended backwards; historical local calendars may differ.