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Clock And Calendar

Hey guys ! It has been a very long time since we have learned something new. So now is the time we should start learning something new. Today I have selected two very basic but useful topics. If anyone of you is preparing for NTSE then these topics are must for your stage 2 Mental Ability. These are 2 very scoring topics which can get you good marks. So now let us begin with the learning.



   

Calendar

So the first topic which are going to study is Calendar. Let us first know how will this help. by learning the tricks of Calendar you can find out the day for a given date. For example : the given date is 26th January,1950. By looking at the date you cannot tell the day but after a few calculations you will be able to.


First thing and the basic thing for Calendar is "odd day". Now you must be wondering odd day means the third day or the fifth day but no. Odd day actually means the number of days left after a whole week is complete.. For better understanding let us take an example. Suppose you are asked to find out how many odd days are there in 45 days. For finding this you will simply divide the given number of days by 7. Why do we do so? We do this because one week completes in seven days, so 45 days actually means 6 weeks and 3 days. Those 3 extra days are known as odd days. Thus we can simply term odd days as the remainder left after diving the given days by 7.

Now you can find the odd days in a year also. So can you find the number of odd days in a year. Simple just divide 365 by 7 and the remainder is 1. So now we know that in a normal year there is 1 odd day and in a leap year there are 2 odd days. Now can you find how many odd days  are there in 100 years? You will first have to find the number of leap years and number of ordinary years and they are : leap year=24 and ordinary year=76. You will think that I have divided wrong but no every century year which is not divisible by 400 is not a leap year. So now calculating the number of odd days : 2 odd days in  a leap year and 1 in an ordinary year. Total= ( 24*2 + 76*1)/7 = 5 odd  days. Similarly in 200 years there are 3 odd days and in 300 years there is only 1 odd day. Now if you calculate for 400 years you will find that there is no odd day. 

So here we learn our second rule that every 400th year will have no odd day i.e. 800 years will have no odd day and so on. And every 100th , 200th and 300th year will have 5, 3 and 1 odd days respectively. So now I hope you can find out the number of odd days given any time period. If yes then congratulations because you have learnt 90% of Calendar. Now we come to the last rule before practicing and that is finding which day is on which odd day. For that you have to follow the table given below
Sunday - 0 odd days
Monday -1 odd day
Tuesday - 2 odd days
Wednesday - 3 odd days
Thursday - 4 odd days
Friday - 5 odd days
Saturday - 6 odd days

Yipee now we are all set to find the days. Let us start by taking the first example which we eventually took



26th January,1950 
For finding the day most simple way is that you divide the given date into different segments and they are
1) Nearest smaller 400th Century
2) Number of centuries 
3) Number of years excluding the given year 
4) All the months before the given month
5) Days in the given month

After you have done this you need to find the number of odd days in each segment and then finally total them and find the last number of odd days.

For the given date it will be 

1600          300             49          26
  0                1               5             5
Total = 11 = 4 odd days 
Therefore it was a Thursday on 26th January,1950.

Now if you were not able to understand then in the above line I have divided the date in the given segments and the lower line has the number of odd days in each segment. For finding the number of odd days in 49 years I first found out the number of leap years and then the number of ordinary years. Number of odd days in 49 years = ( 12*2 + 37*1)/7 = 5 odd  days.

Let us do some practice questions :

2nd October,1869

1600        200       68     Jan   Feb  Mar   Apr    May   Jun   Jul   Aug  Sep   2
  0              3          1       3      0       3       2         3       2     3      3      2      2

Total = 27 = 6 odd days
Therefore it was Saturday on the given date.

Key points to remember :
  • Never forget to consider the leap year. In a leap year February will have 1 odd day.
  • Be careful while dividing the years.
  • Always calculate the total number of odd days never miss any odd day.
  • Every year will repeat itself after 6 years or 11 years.
  • Every year one odd day will be added and in a leap year after February 2 odd days will be added.
I will be discussing the type of questions that come in the exam in the next article with the concepts of clock. Subscribe to our mailing list for daily updates and also follow us on Facebook ( www.facebook.com/highschoolpedia  )forgular news. I hope you enjoyed reading my article and were able to understand the concept thoroughly. If you have any doubt regarding the concept you can mail me at my email is : shivam234agarwal@gmail.com .  In the last I would like to wish you luck for your board exams and have fun reading articles on High School Pedia.

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