Date and Calender

Problems on Date and Calenders are most commonly asked questions these days in competitive examinations. We often see, atleast 2 questions on the same topic. I have seen students spending a lot of time on solving these questions. I received a number of emails over the last few weeks to discuss about this topic. The technique mentioned here is developed over the course of my teaching the students, so I am reasonably you would not find it anywhere.

This will be a pretty long post. Please pay attention while reading through it. If you practice it well, trust me, you can easily get the answer with in 15-20 seconds. I have seen a number of shortcut techniques in the internet. But for that we need to remember a lot of numbers. I am not a big fan of such techniques

One of the most commonly asked question in the examination is :

What day is 24th August 1749 ?

or What day of the week is 17th May 1984 ?

NORMAL AND LEAP Years

As you already know, you have a normal year and leap year. A normal year would have 365 days and a leap year would have 366 days. A leap year comes once every 4 years.

So, a year which is divisible by 4 is considered a leap year. For example, 2004 is divisible by 4. So, it is a leap year. Similarly, the year 1972, 1976 and so on are leap years too. If you donot know how to check if a number is divisible by 4, please refer to my article on Divisible Rules here.

Important : There is an important exception here. For the centenary year like 1000, 1500, 1800, 1900, 2000, in order to check if the centenary year, you need to check if the number is divisible by 400 ( and not 4)

So, 1800 even though is divisible by 4, is not a leap year. Because 1800 is not divisible by 400. However, 1600, 2000, 2400 is a leap year.

TRY YOURSELF

Which of the following years is a leap year ?

1. 1324
2. 1700
3. 2400
4. 1976
5. 1823

Concept of Odd Days

 Days Weeks Odd Days Normal Year 365 52 Weeks + 1 Day 1 Leap Year 366 52 Weeks + 2 Day 2

We already know that a normal year consists of 365 days. That is equivalent to 52 weeks and 1 additional day. For the lack of better word, let us call it the ODD DAY. A normal year would have 1 Odd day.

Similarly a leap year, would have 366 days. That is equivalent to 52 weeks and 2 additional days. A normal year would have 2 Odd days.

For a leap year the number of ODD days is 2 because of an additional day. So there will be a shift of 2 days from year-to-year when there is a leap year So, If Jan 1 2004 is a Monday, then Jan 1 2005 would be a Wednesday.

Finding the day of the week is all about calculating the odd Days

Now, whenever you get a question, where you need to find the day of the week for a particular date, we will calculate the number of odd days for that date. So, whenever, we calculate we divide by 7 and get its reminder which becomes the odd days. From the table, we can easily say the day of the week based on the odd day.

 Number of Odd days Day 0 Sunday 1 Monday 2 Tuesday 3 Wednesday 4 Thursday 5 Friday 6 Saturday

So far so good ?

Now let us remember some important results, which we will use often.

Number of odd days in 100 years

100 years would have 24 leap years ( not 25 as 100th year is not a leap year as long as it is not divisible by 400). So, every 100 years would have 5 odd days.

Number of odd days in 400 years

Number of odd days = 4 x Number of Odd days in 100 years + 1 Odd day( 400th year is a leap year)

Number of odd days = 4 x 5 + 1 = 21 0 3 weeks + 0 odd days.

Number of odd days in 20 years

Every 20 years, you have 15 normal years and 5 leap years ( 4, 8, 12, 16, 20th year is a leap year)

So,

Number of odd days = 15 + 5×2 = 25 = 3 weeks + 4 odd days

Number of odd days in every month of the year

It comes in very handy, if you remember the number of odd days for every month. Depending on the year, any month will have either 28,29, 30 or 31 days.

So, A month with 28 days would have 0 odd days

So, A month with 29 days would have 1 odd days

So, A month with 30 days would have 2 odd days

So, A month with 31 days would have 3 odd days

Notice the pattern in the number of odd days for every month. Now if can remember this pattern of the number of days, you can solve any problem with 15-20 seconds.

Normal Year :

Leap Year :

Now, understand the pattern in the number of odd days.

It is 30 – 32 – 32 – 33 – 23 -23 ( Normal Year)

It is 31 – 32 – 32 – 33 – 23 -23 ( LeapYear)

With this understanding, let us solve some problem.

Example 1 :
What day is 3rd Jan 2012.

Solution :

Number of Odd days in 2000 years = 0

Number of Odd days in 11 years = 9(1) + 2(2) = 13 = 6 odd days

Total number of odd days = 6+3 = 9 = 2 odd days

From the above table, if the number of odd days is 2, then it is Tuesday.

Example 2 :
What day is 15th August 1947?

Solution :

Number of Odd days in 1900 years = 0 ( for 1600 years) + 3×5 = 15 = 1 Odd day

Number of Odd days in 40 years = 4(2) = 1 odd day

Number of Odd days in 6 years = 5 + 2 = 0 odd days

Number of Odd days till July = 3 + 0 + 3 + 2 + 3 + 2 + 3 = 16 = 2 Odd days

15 days in August = 15 = 1 Odd day

Total number of odd days = 1 + 1+ 2 + 1 = 5

From the above table, if the number of odd days is 5, then it is Friday. So,

15th August 1947 is a Friday ( You can remember 15th August 1947 is a Friday as we seen same question in the examination).

Very easy right ðŸ™‚

Example 3 :
What day is October 3rd 1869 ?

Number of Odd days in 1800 years = 0 ( for 1600 years) + 2×5 = 10 = 3 Odd days

Number of Odd days in 60 years = 4(3) = 5 odd day

Number of Odd days in 8 years = 6 + 2×2 = 10 = 3 odd days

Number of Odd days till Sep in 1869 = 3 + 0 + 3 + 2 + 3 + 2 + 3 + 3 + 2 = 21 = 0 Odd days

2 days in October = 2 Odd day

Total number of odd days = 3 + 5 + 3 + 2 = 13 = 6 Odd days

From the above table, if the number of odd days is 4, then it is Saturday.

Very easy right ðŸ™‚

TRY YOURSELF

1. What day is 1 January 1941?
2. What day is 26th June 1983?
3. Find the day on 1st July 1944?
4. Find the day on July 4th 1776?

Kiran Chandrashekhar

Hey, Thanks for dropping by. My name is Kiran Chandrashekhar. I am a full-time software freelancer. I love Maths and Mathematical Shortcuts. Numbers fascinate me. I will be posting articles on Mathematical Shortcuts, Software Tips, Programming Tips in this website. I love teaching students preparing for various competitive examinations. Read my complete story.

1. anurag

Great expalnation, but I think there is a small error. To calculate odd days for 15thAug1947, you took 15days in Aug, but for 3rdOct1869 you took only 2 days in Oct. Which one is correct? Now I know for sure that on 15Aug1947 it was Friday, so second calculation might not be correct.

• Kiran Chandrashekhar

Anurag,
I am sorry, there was a typo. I was supposed to take 2nd October, as you know 2nd October 1869 is the birthday of Mahatma Gandhi ðŸ™‚

2. Vishal

These notes are so helpful 4 me .

3. Nava Das

Thank You