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Day–Date Identification

Introduction

Finding the day of the week for a given date is a common aptitude task. This pattern helps you convert any date into its weekday using simple counting or formulaic shortcuts - a useful skill for calendars, planning, and many competitive tests.

Pattern: Day–Date Identification

Pattern

Convert a given date to its weekday by counting total days (or odd days) from a known reference date and reducing modulo 7.

Step-by-Step Example

Question

What day of the week was 1 January 2020?

Solution

  1. Step 1: Choose a convenient reference date

    Use 1 Jan 2000 = Saturday (a commonly memorized reference). We'll count odd days from 1 Jan 2000 up to 1 Jan 2020.

  2. Step 2: Count full years and find odd days

    From 2000 to 2019 inclusive is 20 years. Count leap years in this span: 2000 (leap), 2004, 2008, 2012, 2016 = 5 leap years. Ordinary years = 20 - 5 = 15. Odd days contribution = (15 × 1) + (5 × 2) = 15 + 10 = 25 odd days.

  3. Step 3: Reduce odd days modulo 7

    25 ÷ 7 → remainder = 25 - (3×7) = 25 - 21 = 4 odd days. This means weekday shifts forward by 4 days from the reference weekday.

  4. Final Answer:

    Wednesday

  5. Quick Check:

    Reference 1 Jan 2000 = Saturday → +4 days → Saturday → Sunday (1) → Monday (2) → Tuesday (3) → Wednesday (4) ✅

Quick Variations

1. Use a nearer reference (e.g., 1 Jan 2010) to reduce counting.

2. Apply month codes or Zeller’s formula for faster single-date computation.

3. For dates within the same year, count month-wise odd days instead of full years.

Trick to Always Use

  • Step 1 → Pick a close reference date you remember (1 Jan 2000 or 1 Jan of a recent year).
  • Step 2 → Convert full years to odd days (ordinary year = 1, leap year = 2), add month odd days, then reduce modulo 7.

Summary

Summary

  • Pick a known reference date and its weekday to start from.
  • Convert elapsed years and months into odd days (ordinary = 1, leap = 2) and sum them.
  • Reduce the total odd days modulo 7 to get the weekday shift.
  • Shift the reference weekday forward by that remainder to get the answer.

Example to remember:
1 Jan 2000 = Saturday → 20 years to 1 Jan 2020 gives 4 odd days → Saturday + 4 = Wednesday.

Practice

(1/5)
1. What day of the week was 1st January 2016?
easy
A. Thursday
B. Friday
C. Saturday
D. Sunday

Solution

  1. Step 1: Choose a reference date

    Take 1 Jan 2000 = Saturday.

  2. Step 2: Count years from 2000 to 2015

    Total = 16 years. Leap years = 2000, 2004, 2008, 2012 = 4. Ordinary = 12. Odd days = (12×1) + (4×2) = 20 → 20 mod 7 = 6.

  3. Step 3: Add 6 days to Saturday

    Saturday + 6 days → Friday.

  4. Final Answer:

    Friday → Option B

  5. Quick Check:

    1 Jan 2016 is known to be Friday ✅
Hint: For every ordinary year add 1 day; for leap year add 2, then reduce modulo 7.
Common Mistakes: Forgetting that 2000 is a leap year (divisible by 400).
2. If 1st January 1995 was Sunday, what day was 1st January 1996?
easy
A. Monday
B. Sunday
C. Tuesday
D. Wednesday

Solution

  1. Step 1: Identify year type

    1995 is an ordinary year (365 days).

  2. Step 2: Find odd days

    365 ÷ 7 leaves remainder 1 → +1 day shift.

  3. Step 3: Apply the shift

    Sunday + 1 = Monday.

  4. Final Answer:

    Monday → Option A

  5. Quick Check:

    Ordinary year moves the date forward by one day → Sunday → Monday.
Hint: Ordinary year → +1 day shift.
Common Mistakes: Using leap-year shift (+2) incorrectly.
3. If 15th August 1947 was Friday, what day was 15th August 1948?
easy
A. Saturday
B. Sunday
C. Monday
D. Tuesday

Solution

  1. Step 1: Identify year type

    1948 is a leap year, and since the date (15 August) is after February, the span includes Feb 29, 1948.

  2. Step 2: Odd days for leap-year span

    Leap-year span → +2 days.

  3. Step 3: Apply the shift

    Friday + 2 = Sunday.

  4. Final Answer:

    Sunday → Option B

  5. Quick Check:

    Leap-year same-date shift after February is always +2 days.
Hint: If the target date is after Feb in a leap year → +2 days.
Common Mistakes: Adding only +1 instead of +2.
4. Find the day of the week on 26th January 1950 (India’s Republic Day).
medium
A. Wednesday
B. Friday
C. Saturday
D. Thursday

Solution

  1. Step 1: Use reference 1 Jan 1900 = Monday

    We will compute total odd days from 1 Jan 1900 to 26 Jan 1950.

  2. Step 2: Count odd days from 1900 to 1949 (50 years)

    Leap years = 1904,1908,1912,1916,1920,1924,1928,1932,1936,1940,1944,1948 = 12.
    Ordinary years = 50 - 12 = 38.
    Odd days = (12×2) + (38×1) = 62 → 62 mod 7 = 6.

  3. Step 3: Add odd days for 1-25 January 1950

    Days passed before 26 Jan = 25.
    25 mod 7 = 4.

  4. Step 4: Total odd days

    6 (years) + 4 (January days) = 10 → 10 mod 7 = 3.

  5. Step 5: Final weekday

    Reference day = Monday.
    Monday + 3 days = Thursday.

  6. Final Answer:

    Thursday → Option D

  7. Quick Check:

    1 Jan 1900 = Monday → +3 odd days gives Thursday → matches historical record (26 Jan 1950).
Hint: Always use (days passed) mod 7, not the date number mod 7.
Common Mistakes: Using 26 mod 7 instead of 25 mod 7, and miscalculating weekday shifts.
5. If 1st March 2021 was Monday, what day was 1st March 2020?
medium
A. Saturday
B. Sunday
C. Monday
D. Tuesday

Solution

  1. Step 1: Identify direction

    We are moving one year backward (2021 → 2020).

  2. Step 2: Determine type of year

    2020 is a leap year, so shift backward by 2 days.

  3. Step 3: Apply backward shift

    Monday - 2 = Saturday.

  4. Final Answer:

    Saturday → Option A

  5. Quick Check:

    Leap year backward → -2 days shift ✅
Hint: Backward across leap → -2 days; across ordinary → -1 day.
Common Mistakes: Adding days instead of subtracting when going backward.

Mock Test

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