There is 1 odd day in 300 years.
Here's how to calculate that:
A normal year has 365 days, which is 52 weeks and 1 day. This extra day is called an "odd day." A leap year has 366 days, which is 52 weeks and 2 days, meaning it has 2 odd days.
To find the number of odd days in 300 years, we need to consider the number of leap years and normal years within that period.
Here's the breakdown:
- Leap Years: Leap years occur every 4 years (with exceptions for century years not divisible by 400). In 300 years, there are typically 300/4 = 75 leap years. However, we need to account for century years that aren't leap years. There are three century years in 300 years: 100, 200, and 300. Since none of these are divisible by 400, none are leap years. Therefore, the number of leap years is 75 - 3 = 72.
- Normal Years: The remaining years are normal years. So, there are 300 - 72 = 228 normal years.
Now, we calculate the total number of odd days:
- Odd days from leap years: 72 leap years * 2 odd days/leap year = 144 odd days
- Odd days from normal years: 228 normal years * 1 odd day/normal year = 228 odd days
Total odd days = 144 + 228 = 372 odd days
To find the equivalent number of odd days, we divide by 7 (since there are 7 days in a week):
372 / 7 = 53 weeks and 1 day.
Therefore, there is 1 odd day in 300 years.
We can also generalize as follows:
- 100 years: 5 odd days
- 200 years: (5 * 2) = 10 => 10 - 7 = 3 odd days
- 300 years: (5 3) = 15 => 15 - (7 2) = 1 odd day
- 400 years: (5 4 + 1) = 21 => 21 - (7 3) = 0 odd days (The "+1" accounts for the fact that the 400th year is a leap year)
