Procedure:
Determine the day of the week for a future date by calculating the total days between dates and identifying "odd days." An odd day is the remainder when total days are divided by 7.
Methodology:
1. Calculate remaining days in the initial month.
2. Calculate days in intervening full months.
3. Calculate days in the target month.
4. Sum all days, divide by 7 for odd days, and add to the starting day of the week.
Example:
Starting date: 1st July 2022 (Sunday). Target date: 1st November 2022.
Days per month:
July: 31 days. Remaining: \(31 - 1 = 30\) days.
August: 31 days.
September: 30 days.
October: 31 days.
November: 1 day (to the 1st).
Total days = \(30 + 31 + 30 + 31 + 1 = 123\) days.
Calculate odd days:
\(123 \div 7\) yields a remainder of 4.
Therefore, there are 4 odd days.
The day on 1st November 2022 is 4 days after Sunday.
Sunday + 4 days = Thursday.
Conclusion:
1st November 2022 was a Thursday.