Episode 8 — Aptitude and Reasoning / 8.18 — Calendar
8.18 Quick Revision - Calendar
Leap Year Rules
Non-century year: Divisible by 4 -> Leap
Century year: Divisible by 400 -> Leap
Examples:
2024 -> Leap (2024/4 = 506)
1900 -> NOT leap (1900/400 != integer)
2000 -> Leap (2000/400 = 5)
Odd Days Table (MEMORIZE)
| Period | Odd Days |
|---|---|
| 1 ordinary year | 1 |
| 1 leap year | 2 |
| 100 years | 5 |
| 200 years | 3 |
| 300 years | 1 |
| 400 years | 0 |
Pattern: 5, 3, 1, 0 (repeats every 400 years)
Day Code
| Odd Days | Day |
|---|---|
| 0 | Sunday |
| 1 | Monday |
| 2 | Tuesday |
| 3 | Wednesday |
| 4 | Thursday |
| 5 | Friday |
| 6 | Saturday |
Month Odd Days (Ordinary Year)
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
3 0 3 2 3 2 3 3 2 3 2 3
For leap year: Feb = 1 (instead of 0)
Algorithm: Find Day of DD/MM/YYYY
Step 1: Century odd days (for completed centuries)
Step 2: Remaining years: (Y + floor(Y/4)) mod 7
Step 3: Completed months' odd days (use table above)
Step 4: Add date (DD)
Step 5: Total mod 7 -> Day code
Same Starting Day Months
Ordinary year:
Jan = Oct
Feb = Mar = Nov
Apr = Jul
Sep = Dec
Leap year:
Jan = Apr = Jul
Feb = Aug
Mar = Nov
Sep = Dec
Calendar Repetition
Ordinary year: repeats after 6 or 11 years
Leap year: repeats after exactly 28 years
Quick Facts
- Ordinary year: starts and ends on same day
- Leap year: ends one day after it starts
- In 400 years: 97 leap years, 303 ordinary years
- 400 years = exactly 146097 days = 20871 weeks
- Same date advances 1 day each ordinary year, 2 days each leap year
Reference Dates
Jan 1, 2000 = Saturday
Aug 15, 1947 = Friday
Jan 26, 1950 = Thursday
Common Mistakes to Avoid
1. 1900 is NOT a leap year (century rule!)
2. 2000 IS a leap year (div by 400)
3. Add 1 odd day for months after Feb in a leap year
4. Odd days = remainder, not total days
5. "Between" dates: clarify inclusive/exclusive