Calendar

 Calendar-based reasoning involves solving problems related to days, dates, months, and years by using standard rules and shortcuts. These questions check your ability to calculate the day of the week for a given date, find odd days, and understand leap years, etc.

📚 Key Concepts You Must Know

🔹 A. Odd Days

• 1 week = 7 days

• Odd days = Number of days more than complete weeks

Example:
10 days = 1 week + 3 days ⇒ 3 odd days

🔹 B. Leap Year vs Ordinary Year

Type	Days	Odd Days
Ordinary Year	365	1
Leap Year	366	2

Leap Year Rule:

• A year divisible by 4 is a leap year

• But if divisible by 100, it must also be divisible by 400 to be a leap year

So 2000 ✅ but 1900 ❌

🔹 C. Day Codes

Day	Code
Sunday	0
Monday	1
Tuesday	2
Wednesday	3
Thursday	4
Friday	5
Saturday	6

🔧 Important Shortcut Methods

✅ Method 1: Finding the Day of a Given Date (Using "Doomsday Rule" or Standard Odd Days Method)

Use the formula:

Day = [ (D + M + Y + (Y/4) ) mod 7 ]

Where:

• D = Date

• M = Month code

• Y = Last two digits of year

• (Y/4) = Quotient (ignore decimal)

• Add century code and adjust for leap years

✅ Month Codes (For Ordinary Year)

Month	Code
Jan	0
Feb	3
Mar	3
Apr	6
May	1
Jun	4
Jul	6
Aug	2
Sep	5
Oct	0
Nov	3
Dec	5

In leap years, Jan = 6 and Feb = 2.

✅ Century Codes

Century	Code
1600	6
1700	4
1800	2
1900	0
2000	6
2100	4

🧩 Solved Examples with Diagrams

🔷 Example 1: What day was 15 August 1947?

Step 1: Split into components

• Date (D) = 15

• Month = August → Month code = 2

• Year = 1947
  → Century code = 0 (1900s),
  → Last 2 digits = 47, (Y = 47), Y/4 = 11

Step 2: Total = D + M + Y + (Y/4) + Century Code
→ 15 + 2 + 47 + 11 + 0 = 75

Step 3: 75 mod 7 = 5 → Friday

✅ Answer: Friday

🔷 Example 2: What day will be on 1 January 2000?

• D = 1

• Month Code = 0 (Jan)

• Y = 00 → Y/4 = 0

• Century code (2000) = 6

→ Total = 1 + 0 + 0 + 0 + 6 = 7 → 7 mod 7 = 0

✅ Answer: Sunday

🔷 Example 3: How many odd days in 400 years?

Every 100 years:

• 1st 100 years = 5 odd days

• 2nd 100 years = 5 odd days

• 3rd 100 years = 5 odd days

• 4th 100 years = 0 odd days (leap year reset)

So:
→ 400 years = 5 + 5 + 5 + 0 = 15 odd days = 1 week + 1 day → 1 odd day

✅ Answer: 1 odd day

🔷 Example 4: Which year will have the same calendar as 2024?

• Check leap/non-leap: 2024 is a leap year

• Next leap year with same calendar = 2052

✅ Answer: 2052

📊 5. Diagram: Day Wheel (Visual Memory Tool)

      Sunday (0)
         |
Wednesday(3) ——— Monday(1)
         |         |
 Saturday(6)     Tuesday(2)
         |         |
    Friday(5) — Thursday(4)

Use this to quickly map final remainders (mod 7 values) to days.

📝 Practice Tip Strategy

Task	Tip
Finding leap years	Use 4 / 100 / 400 rule
Finding same day year	Count years with same odd days
Finding day on future date	Use odd day addition
Fast mental math	Memorize month & century codes

📘 Practice Questions – Calendar

🔹 Q1. What was the day on 26 January 1950?

Step-by-step:

• D = 26

• Month = Jan → Code = 0

• Year = 1950 → Last 2 digits = 50 → 50/4 = 12

• Century Code (1900) = 0

Sum = 26 + 0 + 50 + 12 + 0 = 88
88 mod 7 = 4 → Thursday

✅ Answer: Thursday

🔹 Q2. If 15th August 2023 is Tuesday, what day will it be on 15th August 2025?

• 2023 → Tuesday

• 2024 = Leap year → +2 days

• 2025 = +1 day
  So total = +3 days from Tuesday → Friday

✅ Answer: Friday

🔹 Q3. How many odd days are there in 300 years?

Each 100 years:

• 100 yrs = 5 odd days
  So 300 = 5 + 5 + 5 = 15 odd days
  → 15 mod 7 = 1

✅ Answer: 1 odd day

🔹 Q4. Find the day of the week on 1st January 1901

→ Base year 1900 = Monday (known fact)
→ 1900 was not a leap year → 365 days = 1 odd day
So 1901 = 1 day ahead of Monday = Tuesday

✅ Answer: Tuesday

🔹 Q5. Which year will have the same calendar as 2023?

• 2023 is an ordinary year (not leap)
  → Add 6, find first same odd day pattern year
  → Answer: 2029

✅ Answer: 2029

🔹 Q6. If today is Monday, what will be the day after 121 days?

→ 121 ÷ 7 = 17 weeks + 2 odd days
Monday + 2 = Wednesday

✅ Answer: Wednesday

🔹 Q7. What was the day on 2nd October 1869?

• D = 2

• Month = October → Code = 0

• Year = 69, Y/4 = 17

• Century code for 1800 = 2
  Sum = 2 + 0 + 69 + 17 + 2 = 90
  90 mod 7 = 6 → Saturday

✅ Answer: Saturday

🔹 Q8. If 1st March 2020 was Sunday, what day was 1st March 2019?

→ 2020 was leap → 2 odd days back
→ 1st March 2019 = Sunday − 2 = Friday

✅ Answer: Friday

🔹 Q9. How many leap years are there between 1901 and 2000?

→ Every 4th year:
= (2000 − 1901) ÷ 4 = 99 ÷ 4 = 24.75 → 24 leap years

✅ Answer: 24

🔹 Q10. Find the day on 31st December 1999

• 1900 to 1999 = 100 years

• 100 years = 5 odd days

• Year 1999 = not leap → 365 → 1 odd day
  → Total = 5 + 1 = 6
  Starting from 1 Jan 1900 = Monday
  Monday + 6 = Sunday

✅ Answer: Friday
(Correction: 1 Jan 1900 = Monday → Add 6 odd days → Saturday → 31 Dec 1999 = Friday)

✅ Answer: Friday