User:B. P. de la Calzada/sandbox

Simplified Method in determining the day of the week of a certain date!

Finding Days of a certain date is simply done by finding the remainder of a number divided by seven (7)using the equation;

Wd = Remainder of (Mn+D+Cn+Yn)/7

Where:

(from Mathemagics-How to Look like A Genius! Without Really Trying! By Arthur Benjamin, Ph. D and Michael Brant Shermer, Ph. D))

Jan.,   Mn = 1 (0 for Leap Year)

Feb.. Mn = 4 (3 for Leap Year)

March,  Mn =  4 (for both CY & LY)

April,  Mn =  0 (for both CY & LY)

May,    Mn =  2 (for both CY & LY)

June,   Mn =  5 (for both CY & LY)

July,   Mn =  0 (for both CY & LY)

Aug.,   Mn =  3 (for both CY & LY)

Sept.,  Mn =  6 (for both CY & LY)

Oct.,   Mn =  1 (for both CY & LY)

Nov.,   Mn =  4 (for both CY & LY)

Dec.,   Mn =  6 (for both CY & LY)

Where:

D = date, number from 1 to 31

Cn is determine from the first two digits of the year;

Cn = - 2, when year's first two digits is divisible by 4.

Cn = - 1, when year's first two digits is not divisible by 4 but nearest to it being one (1) less than that year's first two digits divisible by 4

Cn =+ 3, when year's first two digits is not divisible by 4 but nearest to it being one (1) greater than that year's first two digits divisible by 4

Cn =+ 1, when year's first two digits is far from the nearest first two digits that's divisible by 4

Yn = the sum of the last two digits of the year and and it's quarter dropping any remainder.

And when

Wd - 0, Sunday

Wd - 1, Monday

Wd - 2, Tuesday

Wd - 3, Wednesday

Wd - 4, Thursday

Wd - 5, Friday

Wd - 6, Saturday

Example #1: The Inaugural address of the First US President George Washington was delivered on THURSDAY, APRIL 30, 1789;

Mn = 0 ;(April)

D = 30

Cn = +3 ;17/4; not whole number and is nearest to year's whose first two digits has quotient of whole number that is 16 and 17 is greater by 1, therefore Cn = +3.

Yn = Int(89 * 1.25) = 111

Substituting values;

Wd = Remainder of (Mn+D+Cn+Yn) / 7

Wd =(0+30+3+111)/7 = 144/7; 20, Remainder = 4

Wd = 4 = Thursday!!!

Example # 2: The First Inaugural Address of the 16th US President Abraham Lincoln was delivered on MONDAY, MARCH 4, 1861

Mn = 4 (March)

D = 4

Cn = +1 (18 is farther from 16 and 20 the first two digts that are divisble by 4)

Yn = Int(61*1.25) = 76

Then

Wd = MOD(4+4+1+76,7) = 1; therefore Monday

Example #3: The First World War erupted TUESDAY JULY 28, 1914!

Mn = 0, (July)

D = 28

Cn= -1 (19 is nearest to 20 but lesser)

Yn =Int(14*1.25) = 17

Then

Wd = MOD(0+28-1+17,7) = 2, therefore Tuesday

Example #4: The World Day of Peace and New Mellineum SATURDAY JANUARY 01, 2000!

Mn = 0, (January Leap Year)

D  =  1

Cn = -2, (20 divisible by 4)

Yn = Int (00*1.25) = 0

Then

Wd = MOD(0+1-2+0,7) = 6, therefore Saturday!

Note: When month involved is January and February check if the year is Leap Year by doubling the digit before last and add the last digit when divisible by 4; it is! This check is not necessary when last digit is odd number! However when the year's last two digits are zeroes (0) it's leap year when the quotient is whole number after dividing the year by 400!

It should be noted that every 400 years beginning year 1600 January 01 is Saturday!!!

B. P. de la Calzada (talk) 03:38, 18 September 2013 (UTC)