CALENDAR

CALENDAR:

A Calendar is a chart or series of pages showing the days, weeks and months of a particular year, or giving particular seasonal information.

BASIC STRUCTURE OF CALENDAR:

• Ordinary year: Any year which 365 days is called an ordinary year.Ex: 1879, 2009, 2019, etc.

• The division of the number 365 by 7 gives the quotient 52 and remainder 1 which indicates that an ordinary year has 52 weeks and one extra day. This extra day is referred to as an “odd day” throughout the calendar topics.

• Leap year: Any year which has 366 days is called a leap year.Ex: 2012, 2016 2020 etc.

• A leap year has 366 days, the division of the number 366 by 7 gives the quotient 52 and remainder 2. This indicates that a leap year has 52 weeks and 2 extra days. These two extra days are also referred to as “odd days”.

• An ordinary year has one odd day, whereas a leap year has two odd days.

CONCEPTS UNDER CALENDAR:

1) Odd Days: 

• We are supposed to find the day of the week on a given date. 

• For this, we use the concept of 'odd days'.

• In a given period, the number of days more than the complete weeks are called odd days.

2) Leap Year:

• (i). Every year divisible by 4 is a leap year, if it is not a century.

• (ii). Every 4th century is a leap year and no other century is a leap year.

• Note: A leap year has 366 days.

• Examples:   Each of the years 1948, 2004, 1676 etc. is a leap year. Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.

3) Ordinary Year:

The year which is not a leap year is called an ordinary years. An ordinary year has 365 days.

4) Counting of Odd Days:

1 ordinary year = 365 days = (52 weeks + 1 day.)

1 ordinary year has 1 odd day.

1 leap year = 366 days = (52 weeks + 2 days)

1 leap year has 2 odd days.

100 years = 76 ordinary years + 24 leap years

  = (76 x 1 + 24 x 2) odd days = 124 odd days.

  = (17 weeks + days)  5 odd days.

Number of odd days in 100 years = 5.

Number of odd days in 200 years = (5 x 2)  3 odd days.

Number of odd days in 300 years = (5 x 3)  1 odd day.

Number of odd days in 400 years = (5 x 4 + 1)  0 odd day.

Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.

5) Day of the Week Related to Odd Days:

KEY POINTS TO KNOW ABOUT CALENDAR:

• In normal year, 1st january and 31st december has the same days. For example: If the 1st jan is monday then 31st december is also monday.

• In leap year, 1st january is X day then 31st december will be X+1 days. For example: If 1st january is monday then 31st december is tuesday.

• MONTH CODE:

•  YEAR CODE: The series repeats continously

• To find the no.of odd days the year should be divided by 7 , the the remainder of that division is the no.of odd days in a year.

• To find leap year , the century should by divided by 400 where as normal years should be divided by 4, when the remainder is 0 then it is a leap year. Last day of century can not be Tuesday or Thursday or Saturday.

• The calendar of ordinary year repeats after 6 yrs or 11 yrs.

• A Leap year calendar repeats after 28 yrs.

• To know weather the given year is leap year or not we should divide the last two digits of a year with 4, when the remainder is zero then it is leap year , when the remainder is 1,2,or3 it is not a leap year.

• To know weather the given century is leap year or not we should divide the  year with 400, when the remainder is zero then it is leap year , other than zero it is not a leap year.

TYPES OF QUESTIONS:

Type 1: Finding the particular day when date is given.

(Given date + Last two digits of a given year+No.of leap years in the given year(yr divided by 4 and the quotient is ans) + month code + year code)/7.

Note:when it is leap year, and the given month is below March then the answer should be subtracted by 1.

Type 2: Finding the day when another day is not given.

Type 3: Matching the calendars of a month.

Type 4: Repeated Calendar.