5th January 2018 was a Friday.\nWhich of the following future years will also have 5th January falling on a Friday?

Introduction / Context:
This question asks you to determine in which future year a specific date will fall on the same weekday as in a reference year. Here, 5 January 2018 is a Friday, and we must find which given future year also has 5 January on a Friday. Leap years and the number of days in each year determine how weekdays shift from one year to the next.

Given Data / Assumptions:

5 January 2018 is a Friday.

Candidate future years: 2020, 2022, 2023, 2024.

Leap years between 2018 and 2024 follow the rule: divisible by 4 (and for centuries, also by 400).

2018 and 2019 are common years; 2020 is a leap year; 2021, 2022, 2023 are common years; 2024 is a leap year.

Concept / Approach:
To find the weekday of 5 January in a later year, we count how many days elapse between 5 January 2018 and 5 January of the candidate year. Each common year shifts the weekday forward by 1 day, and each leap year shifts it by 2 days, because a leap year has one extra day (366 days). The net shift modulo 7 gives the weekday difference.

Step-by-Step Solution:
Step 1: Calculate year-by-year shifts from 2018 onwards. From 2018 to 2019: 2018 is a common year → shift +1 day. From 2019 to 2020: 2019 is common → +1 day (total +2). From 2020 to 2021: 2020 is leap → +2 days (total +4). From 2021 to 2022: 2021 is common → +1 day (total +5). From 2022 to 2023: 2022 is common → +1 day (total +6). From 2023 to 2024: 2023 is common → +1 day (total +7). Step 2: Reduce total shift modulo 7. Total shift from 2018 to 2024 is +7 days. 7 mod 7 = 0, so the weekday for 5 January 2024 is the same as for 5 January 2018. Therefore, 5 January 2024 is also a Friday.

Verification / Alternative check:
You can verify intermediate years: after +2 days, 5 January 2020 will be two weekdays after Friday, and after +5 days, 5 January 2022 will be five weekdays after Friday. Only when the total shift is a multiple of 7 (such as +7) do we land back on the same weekday. This matches our calculation for 2024, confirming that it shares the same weekday for that date as 2018.

Why Other Options Are Wrong:
For 2020, the total shift from 2018 is +2 days, so 5 January 2020 falls on a Sunday, not Friday.
For 2022, the total shift is +5 days, moving Friday to Wednesday.
For 2023, the total shift is +6 days, moving Friday to Thursday.
Only a shift equivalent to 0 modulo 7 can return the same weekday, which only occurs for 2024 among the options given.

Common Pitfalls:
Learners sometimes mistakenly use the leap-year status of the ending year instead of the year before it when counting the shift or forget to include one of the years in the sum. Another error is assuming a fixed 7-year cycle without accounting for leap years properly. Counting each year’s type (common or leap) and accumulating shifts step by step avoids these mistakes.

Final Answer:
The year in which 5 January again falls on a Friday is 2024.