Calendar Problems - Quick Revision
Calendar Problems - Quick Revision
Key Points (One-Liners)
- Ordinary year = 365 days = 1 odd day; Leap year = 366 days = 2 odd days.
- Every 100 years has 5 odd days (76 ordinary + 24 leap).
- Every 400 years has 0 odd day (multiples of 400 are leap).
- Century leap rule: 400, 800, 1200, 1600, 2000… are leap; 1700, 1800, 1900 are NOT.
- Odd-day cycle: 0-Sun, 1-Mon, 2-Tue, 3-Wed, 4-Thu, 5-Fri, 6-Sat.
- Month codes (non-leap): J F M A M J J A S O N D → 0 3 3 6 1 4 6 2 5 0 3 5.
- Doomsday rule: 4/4, 6/6, 8/8, 10/10, 12/12, 5/9, 9/5, 7/11, 11/7 all fall on same weekday in a year.
- Zeller’s shortcut: (Date + Month-code + Year-last-two + Year-last-two/4) mod 7 → gives weekday.
- Backward/forward in same year: add/subtract days directly; cross-year adjust for odd days.
- Same calendar repeats after 6 or 11 or 28 years depending on leap-pattern.
- 15 Aug every year shifts +1 weekday (+2 in leap).
- 29 Feb exists only in century-multiples-of-400 leap years.
- 100-year block has 76 ordinary + 24 leap → 124 odd days ≡ 5 mod 7.
- 2000-2099 has 25 leap years (2000 is leap, 2100 is not).
- Quick century anchor: 1900-Mon, 2000-Tue, 2100-Sun (memorise).
- First Jan 1 AD was Monday (reference anchor).
- Calendar repeats when total odd days = 0 mod 7.
- Do not count 29 Feb if the date is before 29 Feb in a leap year.
- “Last day” of century = Friday (100 years ≡ 5 odd days → 5th day from Monday).
- RRB favourite: “Find the day of week for given date” → always compute net odd days.
| Formula/Rule | Application |
|---|
| Odd days = (365 × years + leap years) mod 7 | Net days beyond full weeks |
| Leap years = ⌊year/4⌋ – ⌊year/100⌋ + ⌊year/400⌋ | Exact count to avoid over-count |
| Month code + Date + (YY + ⌊YY/4⌋) mod 7 | Weekday from 1 Jan anchor |
| Century offset: 1600-0, 1700-5, 1800-3, 1900-1, 2000-0 | Add to above for any date |
| Doomsday = (2 + 5×(cc mod 4) + YY + ⌊YY/4⌋) mod 7 | Anchor weekday for whole year |
| Same-calendar gap = 6 / 11 / 28 years | Check leap-pattern between years |
| 100 years ≡ 5 odd days | Quick 100-block shift |
| 400 years ≡ 0 odd days | Cycle repeats every 400 yrs |
| 29 Feb → add 1 extra odd day only if date ≥ 29 Feb | Leap-year boundary rule |
Memory Tricks
- “0336 1462 5035” – month codes in order (J-D).
- “5-6-0-1” – century offsets 1700-1800-1900-2000.
- “DOOM” – double-digit dates 4/4, 6/6, 8/8, 10/10, 12/12 always same weekday.
- “FRI-day LAST” – last day of century year (not leap) is Friday.
- “Leap-4, Skip-100, Leap-400” – sing-song to remember leap rule.
Common Mistakes
| Mistake | Correct Approach |
|---|
| Forgetting 2000 is leap but 1900 is not | Check century-divisible-by-400 |
| Counting 29 Feb for January dates | Ignore 29 Feb if date < 29 Feb |
| Using 365.25 blindly for odd days | Use exact leap-year formula |
| Taking 1 Jan 2000 as Sunday | It was Saturday (anchor 0) |
| Adding 1 odd day per 100 years | 100 years give 5 odd days, not 1 |
Last Minute Tips
- Write month codes & century offsets on rough sheet first.
- Always do “mod 7” after every addition to keep numbers tiny.
- For “same calendar” questions, check both leap-year parity and odd-day count.
- If options are close, re-verify whether 29 Feb falls inside the range.
- In 30-second questions, use Doomsday anchor for current year instead of full calculation.
Quick Practice (5 MCQs)
1. What day of the week was 15 Aug 1947?
Friday2. How many odd days are there in 100 years?
53. The calendar for 2028 will repeat next in which year?
20564. If 5 Mar 2009 was Thursday, what was 5 Mar 1985?
Tuesday5. Which of the following is not a leap year? 1600, 1700, 2000, 2400
1700
BETA
