In a certain year January 1st is a Monday, what is the day of the week on April 1st?
Understand the Problem
The question is asking to determine the day of the week for April 1st in a year where January 1st is a Monday. To solve it, we will calculate the number of days from January 1st to April 1st and find the corresponding weekday.
Answer
April 1st is a Sunday.
Answer for screen readers
April 1st is a Sunday.
Steps to Solve
- Count the days in January, February, and March
Since January has 31 days, February has 28 days (assuming it's not a leap year), and March has 31 days, we will sum the days in these three months.
- Days in January: 31
- Days in February: 28
- Days in March: 31
Total days from January 1st to April 1st: $$ 31 + 28 + 31 = 90 $$
- Determine the day of the week for April 1st
Since January 1st is a Monday, we will find out the day of the week after 90 days.
We divide the total days by 7 (the number of days in a week) to find the remainder: $$ 90 \div 7 = 12 \text{ remainder } 6 $$
This means that 90 days is 12 full weeks and 6 extra days.
- Calculate the day of the week
Starting from Monday (day 0), we move forward 6 days:
- Monday (0)
- Tuesday (1)
- Wednesday (2)
- Thursday (3)
- Friday (4)
- Saturday (5)
- Sunday (6)
Thus, April 1st will fall on a Sunday.
April 1st is a Sunday.
More Information
This problem involves basic calendar calculations, considering the number of days in each month as well as the repetitive cycle of weekdays. The leap year is not considered here, simplifying our calculation as 28 days for February.
Tips
- Miscounting the number of days in the months. Always double-check the lengths of the months involved.
- Forgetting to adjust for a leap year if it were applicable.
- Confusing the division and finding the remainder; always ensure to note the correct remainder when calculating the day of the week.
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