Solve Any question on Calendar

Tricks to Solve Calendar 

Today I am going to show you a trick that will help solve the questions of the calendar without resorting to any complicated calculation. We all know that a normal year is 365 days and a leap year is 366 days. each year has whether leap or normal has 52 weeks and each week has 7 days. Now lets first see whether normal and leap years are completely divisible by 7. If we do that we will find that we are left with 1 day as a remainder in a normal year and 2 days as a remainder in a leap year. This is going to form the basis of our concept for finding a day for a given date.

To find a leap year we divide the year by 4 and if it is completely divisible we say it a leap year.  for a century we have to divide it by 400. 

Now if in a year we have 1 odd day ( remaining) and in a leap year we have 2 odd days then the question arises how many days will remain in 100 years. it will not be 100 days as in between we will have the leap years if we do the calculations then we will find that there will be 5 days remaining. Please look at the table below

Years         days remaining

100                5

200               10 days ( 1 week+3 day)

300               15 days(2 weeks +1 day)

400               20 days+ 1 more day for leap year= 21 days which will be 3 weeks so 0 days

now every multiple of 400 years will also have 0 days remaining.

Now let's see how we can use this to solve any question

lets say we are asked what day it was on 1st Jan 2017

Step 1: we have to start from thinking about 2016. as we are talking about 1st jan 2017 We can write 2016 as  2000+16

Step 2: now remember in 2000 we do not have any days remaining ( 2000 is a multiple of 400)

Step 3:  in 16 we will have 4 leap years  and each leap year will have 2 days remaining  so we have 8 days 

Step 4 :  there are 12 normal years so we have 13 days that will be remaining days for each year

Step 5: Add all the days  so we have the following

               2000+16 = 0+8+12 =20 

Remember we are talking about 1st Jan so in this we will add 1 more day hence we have days.

dividing 21/7  we have a remainder of 0 i.e its the 7th day as only in that case you will get a 0

hence 1st Jan 2017 was a Sunday 

An interesting fact to remember is the day on which the normal year starts will also end on the same day However if the year is a leap year then it will end on the day succeeding the day on which it had started

you can check this using calendar..

another fun fact is that the Month of March and November are the same day by day (the starting day will be the same in both), January and October , April and July also have the same calendar.

Points to remember 

- first find the number of days remaining after we have divided the previous year days by 7 

- find the number of odd days if you have been given the number of months by adding all the days and dividing by 0

Hope this will help you in finding out the calendar questions easily and effectively. Contact me if you have a doubt and need clarification