Day After N Days, Leap Years & Repeating Calendars
N दिन बाद कौन-सा दिन, leap year और repeat calendar
Day After N Days, Leap Years & Repeating Calendars
- Calendar
- Day After N Days, Leap Years & Repeating Calendars
Answer day-after-N-days questions, identify leap years (century rule included) and find when a calendar repeats.
🎯 Learning Objective
Answer day-after-N-days questions, identify leap years (century rule included) and find when a calendar repeats.
💡 Concept
- Day after N days = today + (N mod 7) steps forward
- Leap year test: divisible by 4 — but a CENTURY year must be divisible by 400 (2000 yes, 1900 no)
- Same date next year: +1 weekday, or +2 if a 29 February falls in between
- A calendar repeats when the odd days between the two years total a multiple of 7 AND both years are the same type
- Shortcuts: a leap year repeats after 28 years; ordinary years repeat after 6 or 11 years depending on their position after a leap year
🧮 Key Formulas
Day after N days = today + (N mod 7)
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Leap: year ÷ 4; century year ÷ 400
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Repeats: leap year +28; ordinary year +6 or +11
✏️ Easy Example
Q. Today is Monday. What day will it be after 61 days?
- 61 = 7 × 8 + 5 → remainder 5
- Monday + 5 = Saturday
Answer: Saturday
🇮🇳 Real-Life Example
15 August 2025 fell on a Friday. No 29 February comes before 15 August 2026, so Independence Day 2026 falls on Saturday — exactly one odd day ahead.
📝 Exam-Level Example
Q. Which of these are leap years: 1600, 1900, 2024?
- Century years need ÷ 400 → 1600 ✓, 1900 ✗
- 2024 ÷ 4 = 506 and it is not a century → leap
Answer: 1600 and 2024 (1900 is not)
📝 Exam-Level Example
Q. The calendar of the year 2025 will repeat exactly in which year?
- 2025 is the 1st year after leap year 2024
- Rule: 1st year after a leap repeats after 6 years
- Check: odd days 2025-2030 = 1+1+1+2+1+1 = 7 → 0
Answer: 2031
🪄 Memory Trick
Position after a leap year decides the repeat: leap+1 → +6, leap+2 → +11, leap+3 → +11, and a leap year itself → +28. Verify by summing odd days to a multiple of 7.
⚠️ Common Mistakes
- ❌ Declaring 1900 or 2100 a leap year — century years need ÷ 400
- ❌ Adding only 1 day across a 29 February — it needs +2
- ❌ Moving N days instead of N mod 7
🏆 Exam Tips
- ✅ First ask: does a 29 Feb fall inside my counting window?
- ✅ For repeat-calendar MCQs, sum odd days year by year till they hit a multiple of 7
📌 Summary
- After N days → move N mod 7 steps
- Century leap years: only ÷ 400
- Same date next year: +1, or +2 across 29 Feb
- Repeats: leap +28; ordinary +6 or +11