How to Count Odd Days

Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday are the seven days of the week.

An ordinary year has 365 days, but a leap year has 366 days.

In a normal year, February contains 28 days. A leap year, on the other hand, has 29 days in February.

The year is divided into 52 weeks.

Simple method to count odd days

The leap year occurs every 4 years. If a year is divisible by 4 and is not a century then it is a leap year if not it is an ordinary year.

Example: We already know that  leap year was 2012 and even 2008, 2004, and 2000 but 2014 is not a leap year.

There are 2 methods to find if a given year is a leap year or an ordinary year 

Find leap year – Case 1

A leap year is one in which the year’s last two numbers are not equal to zero and are divisible by four.

For example, the year 2012 is a leap year since the last two digits (12) are not equal to zero and 12 is divisible by 4, indicating that the year is a leap year. In the same way, 2016 is a leap year.

Despite the fact that the last two digits (90) are not equal to zero, 1990 is not a leap year. Because 90 is not divisible by 4, it is not a leap year.

Finding leap year – Case 2

If the year’s last two numbers are identical to zero and the year is divisible by 400, the year is clearly a leap year.

For example, the year 2000 was a leap year since the last two digits are zeros and the year is divisible by 400. Similarly, the years 1600 and 1200 were leap years.

1000, on the other hand, was not regarded as a leap year because, despite the fact that the last two digits are zero, 1000 is not divided by 400, hence it is not a leap year.

Odd-day characteristics

There are 366 days in a leap year. In a leap year, February contains 29 days.

There are 52 weeks and 2 odd days in a leap year.

An ordinary year has 52 weeks and one odd day and so it consists of 365 days.

Odd days are important

Odd days help us to calculate  the day of the week for any date. 

We know that for ordinary years, 365 days are there and if we divide 365 days by 7 we will get 1 as the remainder. This means for the ordinary years we have only 1 odd day. Similarly, for a leap year, we will have 2 odd days since there are 366 days in a leap year.

Now, let us find how many odd days a century has.

100 years = 24 leap years + 76 ordinary years

                 = (24×2) + (76×1)        [Odd days]

                 = 48 + 76

                 = 124

When we will Divide 124 by 7 we get the remainder 5.

Therefore, there are 5 odd days in a century.

Similarly, we can calculate the number of odd days in 200, 300 and 400 years.

100 years = 5 odd days

200 years = 2 x 5 = 10 = 3 odd days [ by dividing 10 by 7 we get remainder 3]

300 years = 3 x 5 = 15 days = 1 odd days [by dividing 15 by 7 we get remainder 1]

400 years = 4 x 5 = 20 days + 1     (+1 as 400 is a leap year)

               = 21 days

               = 0 odd days       [by dividing 21 by 7 we get remainder 0]

 Here is a table for odd days

Note! Years divisible by 400 have 0 odd days

Day of the week specifying the odd day’s number

 Conclusion:

We have learned, The number of days more than a complete week is called Odd days. To find the Odd days just divide the given number of days by 7. The remainder that we get after division is the Odd days for the given number of days. Odd days help us to find the day of the week for any date. The leap year occurs once every 4 years. If a year is divisible by 4 and is not a century then it is a leap year if not it is an ordinary year. And there are 2 ways to find a leap year. First, If the last two digits of the year are equal to zero and the year is divisible by 400 then it is definitely a leap year and second If the last two digits of a year are not equal to zero and divisible by 4 then it is a leap year. Last but not least odd days calculations exist so that we can find the day of a week for any given date.