0
0

Day-of-Birth Puzzle

Introduction

Day-of-Birth पहेलियाँ आपको किसी व्यक्ति के जन्म का weekday निकालने के लिए माँगती हैं - इसके लिए उम्र, जन्मदिन, leap years, और weekday संबंधों की जानकारी दी जाती है। ये समस्याएँ सामान्यतः competitive exams में मिलती हैं क्योंकि इनमें odd-day गणना के साथ-साथ समावेशी/बहिष्कृत गिनती और leap-year समायोजन पर भी तर्क लगाना पड़ता है।

Pattern: Day-of-Birth Puzzle

Pattern

मुख्य विचार: आयु के अंतर और दिए गए weekday तथ्यों को कुल odd days (mod 7) में बदलें, उस अंतराल में आने वाले leap years को ध्यान में रखें, और फिर ज्ञात weekday को आगे/पीछे शिफ्ट करके जन्म का weekday निकालें।

Step-by-Step Example

Question

एक व्यक्ति जिसका जन्म 10 January 1990 को हुआ था, उसने अपना 30वाँ जन्मदिन एक Wednesday को मनाया। वह किस weekday पर जन्मा था?

Solution

  1. Step 1: आयु अंतर को वर्षों में बदलें

    उसका 30वाँ जन्मदिन जन्म के 30 साल बाद आता है: 10 Jan 1990 → 10 Jan 2020 (30 साल)।

  2. Step 2: उस अंतराल में leap years गिनें

    1990 से 2019 (inclusive) के बीच के leap years: 1992, 1996, 2000, 2004, 2008, 2012, 2016 → कुल = 7 leap years।

  3. Step 3: कुल odd days निकालें

    Ordinary वर्षों = 30 - 7 = 23 → योगदान = 23 × 1 = 23 odd days.
    Leap वर्षों का योगदान = 7 × 2 = 14 odd days.
    कुल = 23 + 14 = 37। 37 mod 7 → शेष = 2 odd days.

  4. Step 4: शिफ्ट की दिशा तय करें

    30वाँ जन्मदिन का weekday = Wednesday. यह जन्म से 30 साल आगे है, इसलिए जन्म का weekday = Wednesday - (कुल odd days) = Wednesday - 2 दिन = Monday.

  5. Final Answer:

    Monday

  6. Quick Check:

    अगर जन्म का दिन Monday हो तो 30 साल में +2 odd days होने पर Monday + 2 = Wednesday ✅

Quick Variations

1. यदि आयु साल और महीने में दी हो - पहले पूरे साल निकालें, फिर शेष महीनों/दिनों को महीना-वार odd days से संभालें।

2. अगर जन्मदिन उसी वर्ष के अंदर दिए गए weekday से पहले मनाया गया हो तो दिशात्मकता और समावेशिता (inclusive/exclusive) का समायोजन करें।

3. यदि अंतराल शताब्दी सीमाओं को पार करता है तो leap गिनती में शताब्दी नियम (400 से विभाज्य) ध्यान में रखें।

4. यदि किसी विशेष जन्मदिन का weekday दिया है और दूसरे जन्मदिन का weekday पूछ रहे हैं तो उन दो जन्मदिनों के बीच के odd days निकालकर वही तरीका लागू करें।

Trick to Always Use

  • Step 1 → दिए गए जन्मदिन के अंतर को पूरे वर्षों में बदलें (और शेष महीनों/दिनों को अलग रखें)।
  • Step 2 → उस अंतराल के भीतर के leap years ठीक से गिनें (शताब्दी नियम लागू करें)।
  • Step 3 → कुल odd days = ordinary×1 + leap×2 निकालें और mod 7 करें।
  • Step 4 → ज्ञात weekday को जन्म की दिशा में पीछे शिफ्ट करें (यदि आप जन्मदिन से जन्म निकाल रहे हैं) या आगे शिफ्ट करें (यदि जन्म से जन्मदिन निकाल रहे हैं)।

Summary

Summary

  • हमेशा आयु अंतर को सटीक वर्ष-सीमाओं में बदलें और leap years की गिनती सावधानी से करें।
  • Odd-day अंकगणित का उपयोग करें (ordinary = 1, leap = 2) और परिणाम को mod 7 लें।
  • शिफ्ट लागू करते समय दिशा (आगे/पीछे) सही चुनें।
  • त्वरित जाँच के लिए निकाले गए जन्म weekday पर वापस odd days जोड़कर दिए गए जन्मदिन के weekday की पुष्टि करें।

याद रखने के लिए उदाहरण:
Born on Monday → 30th birthday on Wednesday (30-वर्ष के स्पैन में +2 odd days)

Practice

(1/5)
1. A person was born on 5th June 1995. If his 25th birthday fell on a Friday, what day of the week was he born?
easy
A. Wednesday
B. Thursday
C. Tuesday
D. Friday

Solution

  1. Step 1: Calculate years crossed

    From 5 Jun 1995 → 5 Jun 2020 = 25 years.

  2. Step 2: Count leap years

    Leap years between 1996 and 2019: 1996, 2000, 2004, 2008, 2012, 2016 → 6 leap years.

  3. Step 3: Compute odd days

    Ordinary = 19 × 1 = 19; Leap = 6 × 2 = 12; Total = 31 → 31 mod 7 = 3 odd days.

  4. Step 4: Back-calculate birth weekday

    25th birthday = Friday. Birth weekday = Friday - 3 = Tuesday.

  5. Final Answer:

    Tuesday → Option C

  6. Quick Check:

    Tuesday + 3 odd days = Friday ✅
Hint: Count leap years in the completed years, compute odd days, then shift backward from the known birthday.
Common Mistakes: Including the birthday year (2020) when counting completed leap years.
2. A girl celebrated her 20th birthday on Monday in 2023. On what day of the week was she born?
easy
A. Thursday
B. Friday
C. Wednesday
D. Saturday

Solution

  1. Step 1: Determine birth year

    2023 - 20 = 2003.

  2. Step 2: Years crossed and leap count

    From 2003 → 2022 = 20 years. Leap years: 2004, 2008, 2012, 2016, 2020 → 5 leaps.

  3. Step 3: Compute odd days

    Ordinary = 15 × 1 = 15; Leap = 5 × 2 = 10; Total = 25 → 25 mod 7 = 4 odd days.

  4. Step 4: Back-calculate birth weekday

    20th birthday = Monday. Birth weekday = Monday - 4 = Thursday.

  5. Final Answer:

    Thursday → Option A

  6. Quick Check:

    Thursday + 4 odd days = Monday ✅
Hint: Subtract the completed years (end year - age), count leaps, then subtract odd days from given birthday weekday.
Common Mistakes: Counting the birthday year (2023) among the completed years.
3. A man was born on 10th January 1980. If his 40th birthday was celebrated on Friday, which day was his birth date?
easy
A. Tuesday
B. Wednesday
C. Thursday
D. Friday

Solution

  1. Step 1: Duration

    10 Jan 1980 → 10 Jan 2020 = 40 years.

  2. Step 2: Count leap years

    Leap years from 1980 to 2019 inclusive: 1980,84,88,92,96,2000,04,08,12,16 → 10 leaps.

  3. Step 3: Compute odd days

    Ordinary = 30 × 1 = 30; Leap = 10 × 2 = 20; Total = 50 → 50 mod 7 = 1 odd day.

  4. Step 4: Back-calculate birth weekday

    40th birthday = Friday. Birth weekday = Friday - 1 = Thursday.

  5. Final Answer:

    Thursday → Option C

  6. Quick Check:

    Thursday + 1 odd day = Friday ✅
Hint: Count leaps including the starting year if it’s a leap (1980 here).
Common Mistakes: Omitting the starting leap year in the leap count.
4. A person celebrated his 50th birthday on Sunday in 2021. Find the day of his birth.
medium
A. Saturday
B. Sunday
C. Monday
D. Tuesday

Solution

  1. Step 1: Find birth year

    2021 - 50 = 1971.

  2. Step 2: Years crossed and leap count

    From 1971 → 2020 = 50 years. Leap years between 1972 and 2020: 1972, 1976, 1980, 1984, 1988, 1992, 1996, 2000, 2004, 2008, 2012, 2016, 2020 → 13 leaps.

  3. Step 3: Compute odd days

    Ordinary = 50 - 13 = 37 → 37 × 1 = 37; Leap = 13 × 2 = 26; Total = 63 → 63 mod 7 = 0 odd days.

  4. Step 4: Back-calculate birth weekday

    50th birthday = Sunday. Birth weekday = Sunday - 0 = Sunday.

  5. Final Answer:

    Sunday → Option B

  6. Quick Check:

    0 remainder → same weekday → Sunday ✅
Hint: Include century leap-year 2000 and the birthday-year leap (2020) when counting completed years/leaps.
Common Mistakes: Miscounting leap years across century boundaries; off-by-one errors on inclusivity.
5. A person born on 15th August 1975 had his 45th birthday on a Saturday. What day of the week was he born?
medium
A. Saturday
B. Friday
C. Monday
D. Tuesday

Solution

  1. Step 1: Duration

    15 Aug 1975 → 15 Aug 2020 = 45 years.

  2. Step 2: Count leap years

    Leap years between 1976 and 2019: 1976,80,84,88,92,96,2000,04,08,12,16 → 11 leaps.

  3. Step 3: Compute total odd days

    Ordinary = 45 - 11 = 34 → 34 × 1 = 34; Leap = 11 × 2 = 22; Total = 56 → 56 mod 7 = 0 odd days.

  4. Step 4: Back-calculate birth weekday

    45th birthday = Saturday. Birth weekday = Saturday - 0 = Saturday.

  5. Final Answer:

    Saturday → Option A

  6. Quick Check:

    0 remainder → same weekday → Saturday ✅
Hint: If total odd days ≡ 0, weekday stays the same on that anniversary.
Common Mistakes: Forgetting to include the century leap year 2000 in the leap count.

Mock Test

Ready for a challenge?

Take a 10-minute AI-powered test with 10 questions (Easy-Medium-Hard mix) and get instant SWOT analysis of your performance!

10 Questions
5 Minutes