Calendar questions (ASO 2021 and 2025) need just one idea: odd days, the days left over after complete weeks. Once you can count odd days, you can find the day for any date and the year with the same calendar.
Leap years
A year is a leap year if it is divisible by 4. Century years are leap years only if they are divisible by 400: 2000 was a leap year, 1900 and 2100 are not.
Odd days
| Period | Odd days |
|---|---|
| Ordinary year (365 days) | 1 |
| Leap year (366 days) | 2 |
| 100 years | 5 |
| 200 years | 3 |
| 300 years | 1 |
| 400 years | 0 |
Month odd days: 31-day month = 3, 30-day month = 2, February = 0 (or 1 in a leap year).
Day after a given date
Divide the number of days by 7 and move forward by the remainder. Example: 1 January 2007 was a Monday, and 31 January is 30 days later. 30 = 4 weeks + 2, so it is Wednesday (ASO 2021).
Same date next year
The day moves forward by 1, or by 2 if a 29 February falls in between.
Same calendar
Two years have the same calendar when (1) they start on the same day and (2) both are leap years or both are ordinary years. Count the odd days year by year until the total is a multiple of 7. 2007 (ordinary, starts Monday) → 2018 (ASO 2025).
Shortcut: an ordinary year usually repeats after 11 or 6 years, and a leap year after 28 years.