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## #1 2017-05-06 02:45:42

ganesh
Registered: 2005-06-28
Posts: 25,611

### Days and Dates

Days & Dates

Excess days - Number obtained as remainder when divided by 7. e.g. Excess days : remainder when divided by 14 is Nil, ED : remainder when divided by 22 is 1, ED : remainder when divided by 45 is 3 etc.

Fact 1 : January 1, 0001 AD was a Monday.

Fact 2 : Century Factor : 0, 5, 3, 1, 0, 5, 3, 1, 0, 5, 3, 1, 0, 5, 3, 1 ... After 400 years, the days and date repeat itself. For 20th century, it was 1. For 21st century, it is Nil.

Month factor 3 A : Normal years - Jan, Oct - Nil
May - 1
Aug - 2
Feb, Mar, Nov - 3
Jun - 4
Sep, Dec - 5
Apr, Jul - 6.

(This part is primarily of academic interest : (Alternative : Add 1, or Leap years : Optional for the theory part)
Month factor 3 B :
Jan, Apr, Jul - Nil
May - 2
Aug - 3
Feb, Mar, Nov - 4
Jun - 5
Sep, Dec - 6))

Summary: Date can be calculated in this way : Day calculation = Century factor + Month factor + (year - 2) + number of leap years + date.

The reason we calculate (year - 2) is (i) 1 is subtracted for the reason the year is not completed. (ii) We started from 0001 AD. Therefore, we subtract 1 from the present year.
As a result, we subtract 2.
i.e. (year - 2)

For example, day calculation : May 7, 2017 = Century factor = 21st century = 0.
Year factor - 2 = 17 - 2 = 15,
Month factor = May : 1,
Number of leap years = 4 : (16/4); divided by 4 (ignore the decimals).
Day = May 7, i.e. 7.
Total = 0 + 15 + 1 + 4 + 7 = 27.
ED = 6, hence the day is a Sunday.

Another example: Calculation:
Summary: Date can be calculated in this way : Century factor + Month factor + (year - 2) + number of leap years + date.
For example, day calculation : Oct 27, 1965 = Century factor = 20th century = 1.
20th century, Year factor = 65 - 2 = 63.
Month factor = October = Nil
Number of leap years = 16
Day = 27.
Total = 107, Excess days = 2, i.e. Wednesday.

Third example:
Day calculation : Oct 2, 1869
Century factor = 19th century = 3
Year factor = (69 - 2) = 67.
Month factor = Oct = Nil
Number of leap years = 17
Day = 2
Total = 3 + 67 + 0 + 17 + 2 = 89
Excess days = 5, i.e. Saturday.

Fourth example:
Day calculation : December 25, 2017
Century factor = 21st century = 0
Year factor - 2 = 17 - 2 = 15
Month factor = December = 5
Number of leap years = 4
Day = 25
Total = 0 + 15 + 5 + 4 + 25 = 49
Excess days = Nil, that is, Monday.

Last edited by ganesh (2017-05-07 00:26:02)

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