Using 5th June 2022 (a Sunday) as our reference date, let’s determine which date in June 2099 will fall on a Sunday.

Step-by-Step Calculation

1. Counting the Years and Days: The difference between 2022 and 2099 is 77 years. Each ordinary year adds 1 day to the calendar, and each leap year adds 2 days. Among these 77 years, we have 58 normal years and 19 leap years (since a leap year occurs every 4 years, $77 \div 4 = 19$).

2. Calculating Total Days Added: Days added by normal years: $58 \times 1 = 58$ Days added by leap years: $19 \times 2 = 38$ Total days added = $58 + 38 = 96$

3. Finding the Day of the Week in June 2099: Dividing 96 by 7 gives a remainder of 5, meaning 5 extra days beyond a full week cycle. Starting from 5th June 2022 (a Sunday) and adding 5 days brings us to Friday. Therefore, 5th June 2099 will fall on a Friday.

4. Finding the Nearest Sunday in June 2099: Moving forward from 5th June 2099 (Friday), the next Sunday will be 7th June 2099.