# The Calendar

## CONCEPT

We are to find the day of the week on a mentioned date. Certain concepts are defined as under.

### ODD DAYS

The no. of days exceeding the complete no. of weeks in a duration is the no. of odd days during that duration.

### ORDINARY YEAR

An ordinary year has 365 days.

### LEAP YEAR

A leap year has 366 days. Every year which is divisible by 4 is called a leap year. For example 1200, 1600, 1992, 2004, etc. are all leap years.

 The First year of every century year ending in 00's but not a multiple of 400 is not considered a leap year. For example 900,1000, 1100, 1300, 1400, 1500, 1700, 1800, 1900, 2100 are not leap years.

### COUNTING OF ODD DAYS

(i) Every Ordinary year has 365 days = 52 weeks + 1 day ∴ (ordinary year has 1 odd day).

(ii) Every leap year 366 days = 52 weeks + 2 days ∴ (leap year has 2 odd days).

(iii) 100 years = 76 ordinary years + 24 leap years ( The year 100 is not a leap year)

= 76 odd days + 2 × 24 odd days = 124 odd days.

124/7 = 5 (Remainder) = 05 odd days

Similarly, 200 years = 10 odd days = 03 odd days

300 years = 15/7 = 01 odd day

400 years = 20 + (1)/7 = 0 odd day {1 is added as 400 is a leap year}

Similarly, 800, 1200, 1600, 2000, 2400 years contain 0 odd days

### COUNTING OF DAYS

After counting the odd days, we find the day according to the no. of odd days → Sunday for 0 odd day, Monday for 01 odd day and so on.

 In an Ordinary Year, First & last day of the year are the same. (i) If 1 Jan is Friday than 31 Dec. will also have Friday. (ii) For a leap year, if first day is Monday then last day will be Tuesday for the same year. (iii) Calendar year 1 Jan to 31 Dec. Financial year 1 April to 31 March. (iv) The day on which calendar Started i.e., 1 Jan, 001 was Monday. (v) In a Leap year, February is of 29 days. In an ordinary year, February has 28 days

### YEAR TABLE

 Ordinary Year – 365 days Leap Year – 366 days January 31 January 31 February 28 February 29 March 31 March 31 April 30 April 30 May 31 May 31 June 30 June 30 Total 181 days Total 182 days July 31 July 31 August 31 August 31 September 30 September 30 October 31 October 31 November 30 November 30 December 31 December 31 Total 184 days Total 184 days

### CALCULATING ODD DAYS

 Month Jan Feb March April May June July Aug Sep Oct Nov Dec Odd days 3 0/13 ord./Leap yr 3 2 3 2 3 3 2 3 2 3
 Months of years Ist three months (1 Jan to 31 March) IInd three months (1 Apr to 30 June) IIIrd three months (1 July to 30 Sep.) IVth (last) three months Total year (1 Jan. to 31 Dec.) Total days 90 / 91 ord. / leap 91 92 92 365/366 ord./leap Odd days 6 / 0 ord. / leap 0 odd day 1 odd day 1 odd day 1 / 2 odd days