To determine the day of the week for 1st January 2022, given that 1st January 2021 was a Friday, follow these steps.
Step 1: Determine the number of days between the two dates
The duration between 1st January 2021 and 1st January 2022 is equivalent to the total number of days in the year 2021.
Step 2: Verify if 2021 is a leap yearA standard year comprises 365 days.
A leap year contains 366 days.
A year is classified as a leap year if it is perfectly divisible by 4, unless it is divisible by 100 but not by 400.Evaluation for 2021:\[2021 \div 4 = 505 \text{ remainder } 1\]Since 2021 is not divisible by 4,
2021 is a normal year.\[\text{Number of days in 2021} = 365\]Step 3: Calculate the number of odd daysFor a normal year, the number of odd days is calculated as:\[365 \text{ days} = 52 \text{ weeks} \times 7 \text{ days/week} + 1 \text{ day}\]\[= 364 + 1\]A normal year thus has 1 odd day.
Step 4: Compute the day of the week
If a specific date in a standard year falls on a certain day of the week, the corresponding date in the subsequent year will advance by one day (modulo 7).
Given: 1st January 2021 was a Friday.
As 2021 has 1 odd day, 1st January 2022 will be:\[\text{Friday} + 1 = \boxed{\text{Saturday}}\]