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**ganesh****Moderator**- Registered: 2005-06-28
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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 : 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 - NilMay - 2Aug - 3Feb, Mar, Nov - 4Jun - 5Sep, Dec - 6))*

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

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 6, i.e. 6.

Total = 0 + 15 + 1 + 4 + 6 = 26.

ED = 5, hence the day is a Saturday.

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.

*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)*

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

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