5 January 2018 was a Friday. Which of the following given years will also have 5 January falling on a Friday?

Introduction / Context:
This question deals with the repetition of specific date and weekday combinations in future years. We know that 5 January 2018 was a Friday, and we are asked which of the given years will again have 5 January on a Friday. This problem reinforces how weekdays shift from year to year depending on whether intervening years are leap years or ordinary years.

Given Data / Assumptions:

• 5 January 2018 is a Friday.
• Candidate future years are 2022, 2020, 2024, and 2023.
• We apply standard Gregorian leap year rules: years divisible by 4 are leap years except certain century years.
• We must track weekday shifts from 2018 to each candidate year and see where 5 January aligns again with Friday.

Concept / Approach:
From one year to the next, the weekday for a given date usually shifts by one day forward (since 365 mod 7 = 1). If the year in between is a leap year and our date occurs after 29 February, the shift becomes two days forward (because 366 mod 7 = 2). To find when the same date repeats its weekday, we accumulate these shifts over successive years and look for when the total shift is a multiple of seven days. That year will have the same weekday for that date.

Step-by-Step Solution:
Step 1: Determine which of the years between 2018 and each candidate year are leap years. Step 2: The leap years in this range include 2020 and 2024, while 2019, 2021, 2022, and 2023 are ordinary years. Step 3: From 2018 to 2019, the weekday for 5 January shifts by 1 day because 2018 is an ordinary year and 5 January is before any leap day of that year. Step 4: Continuing this reasoning and summing the one day and two day shifts for ordinary and leap years respectively, it turns out that by 2024, the cumulative shift equals a multiple of 7 days. Step 5: Therefore, the calendar in 2024 lines up so that 5 January once again falls on Friday.

Verification / Alternative check:
You can confirm this by directly checking the weekday for 5 January 2024 in a reliable calendar or by using a date to weekday algorithm. Doing so will show that 5 January 2024 is indeed a Friday. For the other candidate years, such as 2020, 2022, and 2023, the cumulative day shifts do not sum to a multiple of 7, and their 5 January dates fall on different weekdays. This confirms that only 2024 satisfies the required condition.

Why Other Options Are Wrong:
In 2020, the shift from 2018 has not yet cycled through a full multiple of 7 days, so 5 January 2020 does not fall on a Friday. Likewise, years 2022 and 2023 continue to have weekdays for 5 January that are offset by one or more days from Friday due to the sequence of ordinary and leap years in between. Since their net shifts from 2018 are not multiples of 7, they cannot match the same date and weekday combination.

Common Pitfalls:
One common mistake is to assume that weekdays repeat every 7 years for any date. This naive rule ignores the effect of leap years. When leap years appear between the years you are comparing, they cause an extra shift of one day, altering the pattern. Another error is to treat every year as if it added only one day to the weekday shift, which is not correct once leap years are involved. Always count leap years and add two day shifts for dates after 29 February in those years.

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