Discussion
5th January 2018 was a Friday. Which of the following years will also have 5th January on a Friday?
Answer: C
Only the remainder on division by 7 matters - the odd days.
Track the weekday of 5 January year by year. An ordinary year adds one day; a leap year adds two, but only if 29 February falls within the interval - which it does for the year following a 5 January in a leap year.
\[ 2018 \text{ Fri} \to 2019 \text{ Sat} \to 2020 \text{ Sun} \to 2021 \text{ Tue} \]
\[ \to 2022 \text{ Wed} \to 2023 \text{ Thu} \to 2024 \ \textbf{Fri} \]
The jump from 2020 to 2021 skips Monday because 29 February 2020 lies between the two dates.
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