Calendar

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Calendar — Key Facts for SSC CGL • Every year has 365 days (52 weeks + 1 day). A leap year has 366 days (52 weeks + 2 days). • Leap Year Rule: A year divisible by 4 is a leap year except century years (divisible by 100), unless also divisible by 400.

• 2000 → Leap (divisible by 400) ✓; 1900 → Not leap (divisible by 100 but not 400) ✗
• 2024 → Leap (divisible by 4) ✓ • Odd Days: The extra days beyond complete weeks. 365 ÷ 7 = 52 weeks + 1 odd day. 366 ÷ 7 = 52 weeks + 2 odd days. • Days of the Week cycle: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday — then back to Monday. • Reference date to memorise: 1 January 1 AD was a Monday (or use 1 March 0000 as reference in the standard algorithm). • For any date: Count odd days from a known reference, then find the day.

⚡ Exam Tip: Learn the day codes: Sunday=0, Monday=1, Tuesday=2, Wednesday=3, Thursday=4, Friday=5, Saturday=6. Then use: $(\text{Reference Day Code} + \text{Total Odd Days}) \mod 7$ to find the day. This method handles all calendar questions in under 60 seconds.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Calendar — SSC CGL Study Guide

Core Concept: Calendar problems ask you to find the day of the week for a given date, or to count how many times a particular day falls in a given month/year. The key is understanding odd days and how they accumulate over years.

Step-by-Step Method to Find Day for Any Date:

1. Calculate total days from a reference year (e.g., 1 March 0000).
2. Add odd days from completed years before the target year.
3. Add odd days for months in the target year (before the target month).
4. Add the day of the month.
5. Take modulo 7 to get the day code, then convert to day name.

Odd Days Contribution by Year:

Year Type	Days in Year	Odd Days Added
Normal year	365	1
Leap year	366	2

Odd Days Contribution by Month (non-leap year): Jan:31→3, Feb:28→0, Mar:31→3, Apr:30→2, May:31→3, Jun:30→2, Jul:31→3, Aug:31→3, Sep:30→2, Oct:31→3, Nov:30→2, Dec:31→3

Odd Days Contribution by Month (leap year): Feb:29→1 (instead of 0); all others same as above.

Worked Example: Find the day on 15 August 1947 (India’s Independence).

• Base: 1 March 0000 = Monday
• Years 0 to 1946: Count normal and leap years
  • 1946 ÷ 4 = 486 leap years; 1946 ÷ 100 = 19 century years; 1946 ÷ 400 = 4 divisible by 400
  • Actual leap years = 486 − 19 + 4 = 471 leap years
  • Normal years = 1946 − 471 = 1,475 normal years
  • Odd days = $1{,}475 \times 1 + 471 \times 2 = 1{,}475 + 942 = 2{,}417$ odd days
  • $2{,}417 \mod 7 = 2{,}417 - 7 \times 345 = 2{,}417 - 2{,}415 = 2$ odd days
• Months in 1947 before August: Jan(3) + Feb(0, 1947 not leap) + Mar(3) + Apr(2) + May(3) + Jun(2) + Jul(3) = 16 odd days → 16 mod 7 = 2
• Day of month: 15 → 15 mod 7 = 1
• Total odd days: 2 + 2 + 1 = 5 → Code 5 = Friday

Common Student Mistakes: Forgetting the leap year exception (century not divisible by 400), counting the month itself instead of months before it, and miscounting odd days in January/February for leap years.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Calendar — Comprehensive SSC CGL Notes

Theoretical Foundation: The Gregorian calendar system was introduced in 1582 by Pope Gregory XIII to correct the Julian calendar’s drift. India adopted it in 1957 when the British standardized the calendar across colonies. For SSC CGL, calendar questions test rigorous modular arithmetic under time pressure.

Century Codes (useful shortcut for calendar calculations):

Century	Code
1600-1699	0
1700-1799	5
1800-1899	3
1900-1999	1
2000-2099	6

Alternative: Zeller’s Congruence (Simplified for SSC CGL): For any date, the day code can be found using: $$h = \left(q + \left\lfloor\frac{13(m+1)}{5}\right\rfloor + K + \left\lfloor\frac{K}{4}\right\rfloor + \left\lfloor\frac{J}{4}\right\rfloor - 2J \right) \mod 7$$ Where: q = day of month, m = month (3=March…14=February), Y = year (adjust month Jan/Feb as month 13/14 of previous year), K = year of century (Y mod 100), J = century (Y div 100).

Advanced Worked Example: Find all leap years between 1900 and 2000 where 1st September is a Wednesday.

• Years divisible by 4: 1904, 1908, 1912, …, 1996, 2000
• Subtract century exceptions: 1900 is not a leap year, 2000 is (div by 400)
• For each leap year, compute odd days from Jan 1 to Aug 31
• August has 31 days → 3 odd days
• If total odd days from 1 Jan gives Wednesday for 1 Sep, find matching years
• This type of exhaustive question appears in SSC CGL Tier-II

Most Likely Day Combinations:

• 1st January falls on a Tuesday most frequently in the 20th century
• February 29 falls on a Monday, Wednesday, or Friday most often in the 1900s

SSC CGL PYQ Pattern (2019-2023):

• 2023 Tier-I: 1 calendar question (finding day for a historical date like 1947 or 1950)
• 2022 Tier-I: 1 question (counting Tuesdays in a month)
• 2021 Tier-I: 2 questions (leap year identification + day calculation)
• Leap year exception (century years) is the #1 trap in these questions
• Most difficult variant: “If yesterday was 3 days after Friday” type questions

Master Formula: Count total odd days from a known reference, then $(\text{Reference Day} + \text{Total Odd Days}) \mod 7 = \text{Target Day}$.

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