Solving the Day of the Week Problem

The question asks us to determine the day of the week for 8th June, 2036, given that 8th June, 2037, is a Sunday. We need to work backward by calculating the number of days between these two specific dates.

Calculating the Day Shift

1. Identify Dates: We have two dates: 8th June, 2037 (Sunday) and the target date 8th June, 2036.
2. Determine Period Length: The time difference is exactly one year. We need to find the number of days between 8th June, 2036, and 8th June, 2037.
3. Check for Leap Day: The year 2036 is a leap year (divisible by 4). However, the leap day, February 29th, 2036, occurs *before* the starting date of 8th June, 2036. The period we are considering (from 8th June 2036 to 8th June 2037) does not include February 29th. Therefore, the total number of days in this specific one-year period is 365.
4. Calculate Day Change: A normal year has 365 days. To find the shift in the day of the week, we calculate the remainder when 365 is divided by 7:

   $ 365 \mod 7 $

   $ 365 = (52 \times 7) + 1 $

   The remainder is 1. This means that a date shifts forward by 1 day after a 365-day period.

5. Work Backward: Since the day shifts forward by 1 day from 2036 to 2037, we must shift backward by 1 day from 8th June, 2037, to find the day for 8th June, 2036.
6. Final Calculation: The known day is Sunday (8th June, 2037). Going back 1 day from Sunday:

   Sunday - 1 day = Saturday

Therefore, 8th June, 2036, was a Saturday.