To celebrate the first day of a leap year, I taught my dog to jump through a hoop. It was a Sunday. When he taught me the same trick the first day of the next year, it was a ?
A. Sunday
B. Monday
C. Tuesday
D. Wednesday
So whats the answer tuesday?
To determine the day of the week for the first day of the next year, we need to understand the leap year pattern. A leap year occurs every four years, except for years that are divisible by 100 but not divisible by 400.
Since we are celebrating the first day of a leap year and it was a Sunday, we can deduce that it is either January 1st or January 8th of that year (since the first day of a leap year can fall on either of these days when it starts on a Sunday).
Next, we need to know that there are 365 days in a year, or 366 days in a leap year. This means that January 1st of the next year will be 365 days ahead of the first day of a leap year, and January 8th of the next year will be 372 days ahead.
Since both 365 and 372 are divisible by 7 (the number of days in a week), we know that the first day of the next year will fall on the same day of the week as the first day of the leap year.
Therefore, the answer is A. Sunday.
To determine the answer, we need to understand how leap years and days of the week are related. A leap year occurs every four years, which means it has an extra day, February 29th.
To figure out the day of the week for a specific date, we can use a method called the Zeller's Congruence. It involves a series of mathematical calculations based on the year, month, and day.
Let's break it down step by step. The formula for Zeller's Congruence is:
h = (q + [(13(m + 1)) / 5] + K + [K / 4] + [J / 4] − 2J) % 7
- h represents the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, and so on).
- q is the day of the month.
- m is the month (3 = March, 4 = April, and so on; it treats January and February as months 13 and 14 of the previous year).
- K is the year of the century (i.e., year % 100).
- J is the zero-based century (year / 100).
Now, we'll apply this formula step by step for both scenarios:
1. First day of the leap year:
- Since it's a leap year, the date is February 29th, which can be represented as 29/2/leap year.
- In this case, m = 14 (treating February as the 14th month), q = 29, and K and J depend on the specific leap year.
- Plug these values into the formula to calculate h.
- Once you have h, you can determine the corresponding day of the week using the values 0 to 6.
2. First day of the next year:
- Since it's the first day of the year, the date is January 1st, which can be written as 1/1/next year.
- In this case, m = 1, q = 1, and K and J depend on the specific next year.
- Plug these values into the formula to calculate h.
- As before, use the value of h to determine the day of the week.
By applying these calculations for both scenarios, you will be able to find the day of the week for each date and answer the question correctly.
In general, days of the week advance one day per year (on the same day/month). For leap years, days from first of January to the 28th of February will jump TWO days if it is a leap year.
For example, January 1st 1900 was a Monday. January 1st 1901 was a Tuesday (note that 1900 was NOT a leap year).