Calendar Questions

Calendar Questions need a lot of practice to solve the problems. Although the frequency of this question is less in exams they are of equal importance. If you have learned the basics of these questions than it will become very easy for you to solve it. You can be asked whether the year mentioned in the question is a leap year or not! You will be given a date and a day and you will be asked to determine the day that will fall on the same date on next year and many more.

Let us begin with the basics. We know that in an ordinary year there are 365 days, which means 52 × 7 + 1, or 52 weeks and one day. This additional day, we call an odd day. If 1st January of this year is on Sunday, then 1st January next year will be exactly 52 full weeks and a day after that – so on a Monday.

This is all right as long as the year is not a leap year. The Earth actually completes 1 orbit around the Sun in more than 365 days, i.e in 365 Days 5 Hours 48 minutes and 45 seconds or takes approximately 6 hours more. A leap year occurs every 4 years to adjust for the 1/4th day, 6 x 4= 24 hours, so every 4th year has 366 days (or 2 odd days). And as far as the few odd minutes of the orbit time are concerned, well every 100 years starting 1 AD, the year is declared to be a non–leap year, but every 4th century is a leap year. So any year divisible by 400 will be a leap year e.g.: 1200, 1600 and 2000. The years 1800, 1900 will be non leap years.

Odd Days Concept

Suppose we have to calculate the number of odd days in 1200 years. In 1200 there are 3 years which are divided by 100 and 400. (400, 800, and 1200). And the remaining years are only divided by 100. (100, 200, 300, 500, 600, 700, 900, 1000, and 1100). Every 100 years have 76 ordinary years and 24 leap years.

Odd days in ordinary year = (52 weeks + 1) days. Odd days in a leap year = (52 weeks +2) days. So odd days in 100 years will be (76 x 1 + 24 x 2) which is 124 odd days. This can also be written as 17 weeks + 5 days. So every 100 years will have 5 odd days. Similarly, 200 years will have (5 x 2) = 3 odd days and 300 years will have 1 day.

The number of odd days in 400 years will be ( 5 x 4 + 1) because 400 is itself a leap year and that is why it has one odd day extra. Thus odd days in 400 will be 0. This is the same for every year which is a multiple of 100 and 400. Thus 1200 will also have odd days. Now we will solve some examples to have a better understanding of this, concept.