Calculating Day of Week for $26^{\text{th}}$ September
The problem requires finding the day of the week for $26^{\text{th}}$ September, given that $12^{\text{th}}$ August was a Monday in the same year. We need to calculate the total number of days between these two dates.
Days Remaining in August
First, calculate the number of days remaining in August after the $12^{\text{th}}$.
- Total days in August = 31
- Days remaining = Total days - Given date
- Days remaining = $31 - 12 = 19$ days
Days in September
Next, count the number of days in September up to the target date.
- Days in September = 26 days
Total Number of Days
Sum the days remaining in August and the days in September.
- Total days = Days remaining in August + Days in September
- Total days = $19 + 26 = 45$ days
Calculating the Day Shift
To find the day of the week, calculate the remainder when the total number of days is divided by 7 (since there are 7 days in a week).
- Day shift = Total days $\mod 7$
- Day shift = $45 \mod 7$
- $45 = (6 \times 7) + 3$
- Day shift = 3
A remainder of 3 means the day will shift forward by 3 days from the starting day.
Determining the Final Day
The starting day ($12^{\text{th}}$ August) was Monday. Add the calculated day shift.
- Starting day: Monday
- Shift: +3 days
- Monday + 1 day = Tuesday
- Monday + 2 days = Wednesday
- Monday + 3 days = Thursday
Therefore, $26^{\text{th}}$ September will be a Thursday.
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