Introduction / Context:
Repeating calendar questions ask you to identify which year has the same arrangement of weekdays and dates as a given base year. For two years to have identical calendars, they must both be leap or non leap years and the total number of odd days between them must be a multiple of 7. Here, we are asked to find a future year whose calendar matches that of 2018.
Given Data / Assumptions:
- Base year: 2018.
- Candidate years: 2023, 2027, 2029, 2022.
- 2018 is a non leap year.
- We use Gregorian leap year rules.
Concept / Approach:
We examine the years after 2018 and tally odd days contributed by each year. A non leap year contributes 1 odd day; a leap year contributes 2 odd days. We are looking for a year in which the cumulative odd days from 2018 up to that year sum to a multiple of 7 and where the candidate year itself is also a non leap year. Among the options, we must identify the earliest year that satisfies these conditions.
Step-by-Step Solution:
Check the leap status of the candidate years.
Year 2018: non leap, 2019: non leap, 2020: leap, 2021: non leap, 2022: non leap, 2023: non leap, 2024: leap, 2025: non leap, 2026: non leap, 2027: non leap, 2028: leap, 2029: non leap.
We need a non leap year candidate where the total odd days from 2018 up to that year are divisible by 7.
Counting from 2018 to 2029, we find that the pattern of odd days leads to a total shift that brings the weekdays back into alignment in 2029.
Standard calendar tables confirm that 2018 and 2029 share the same calendar layout.
Verification / Alternative check:
By direct calendar comparison, 1 January 2018 and 1 January 2029 fall on the same weekday.
Both years are non leap years, so the lengths of all months match exactly.
As a result, every date from January to December in 2029 falls on the same weekday as the corresponding date in 2018.
Why Other Options Are Wrong:
Option A (2023): Although non leap, its weekday pattern does not align with 2018 for all months.
Option B (2027): Also non leap, but still does not yield an exact calendar match when checked month by month.
Option D (2022): Too close, with odd days not summing to a multiple of 7 from 2018.
Option C (2029): Correct, since 2018 and 2029 share the same full calendar.
Common Pitfalls:
Relying only on approximate rules without checking the leap year distribution can give wrong answers.
Some learners confuse the 11 year and 6 year cycles without verifying them for a specific range.
Not verifying that both years are of the same leap type is another frequent mistake.
Final Answer:
The calendar for 2018 will be the same as that for 2029.
Discussion & Comments