The question asks to find the day of the week for January 12, 2022, given that March 21, 2021, was a Sunday.
Start Date Day Number
First, calculate the day number of the start date, March 21, 2021, in the year 2021. Assume January 1st is day 1.
- Days in January = 31
- Days in February = 28 (2021 is not a leap year)
- Days in March = 21
Day number for March 21, 2021 = $31 + 28 + 21 = 80$. The $80^{\text{th}}$ day of the year.
Remaining Days 2021
Calculate the number of days remaining in the year 2021 after March 21.
Total days in 2021 = 365.
Remaining days = Total days - Day number of March 21
Remaining days = $365 - 80 = 285$ days.
Days Passed 2022
Calculate the number of days passed in the target year, 2022, until the target date (January 12, 2022).
Days in January = 12.
So, 12 days have passed in 2022.
Total Duration Odd Days
Calculate the total number of days between March 21, 2021, and January 12, 2022.
Total Duration = (Remaining days in 2021) + (Days passed in 2022)
Total Duration = $285 + 12 = 297$ days.
Now, find the number of odd days by calculating the remainder when the total duration is divided by 7.
Odd Days = $297 \pmod 7$
$297 = (42 \times 7) + 3$
The remainder is 3. So, there are 3 odd days.
Final Day Determination
The starting day, March 21, 2021, was a Sunday.
Add the number of odd days to the starting day.
Final Day = Sunday + 3 days
Sunday + 1 day = Monday
Sunday + 2 days = Tuesday
Sunday + 3 days = Wednesday
Therefore, January 12, 2022, will be a Wednesday.
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