The calendar for the year 2019 will be the same as the calendar for which of the following year?
The calendar for the year 2019 will be the same as the calendar for which of the following year?
Solution
For calendars to be identical, two conditions must be met:
- Both years must start on the same day of the week
- Both years must have the same type (both leap years or both non-leap years)
2019 is not a leap year since it's not divisible by 4.
A regular year has 365 days = 52 weeks + 1 day, so the next year starts 1 day later in the week.
A leap year has 366 days = 52 weeks + 2 days, so the next year starts 2 days later in the week.
Counting the day shift from 2019:
2019 → 2020 (leap year): shifts by 2 days
2020 → 2021: shifts by 1 day (total: 3 days)
2021 → 2022: shifts by 1 day (total: 4 days)
2022 → 2023: shifts by 1 day (total: 5 days)
2023 → 2024 (leap year): shifts by 1 day (total: 6 days)
2024 → 2025: shifts by 2 days (total: 8 days ≡ 1 day mod 7)
2025 → 2026: shifts by 1 day (total: 2 days)
2026 → 2027: shifts by 1 day (total: 3 days)
2027 → 2028 (leap year): shifts by 1 day (total: 4 days)
2028 → 2029: shifts by 2 days (total: 6 days)
2029 → 2030: shifts by 1 day (total: 7 days ≡ 0 days mod 7)
After 7 days of shift (one complete week), the starting day returns to the same day as 2019.
2030 is not divisible by 4, so it's not a leap year, matching 2019.
Therefore, the calendar for 2019 will be the same as 2030.
The answer is Option 2: 2030.
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