[Math4u] Just for Christmas fun

There is generally a calculational formula extant to locate holidays in various calendars.  For example, in the Christian Calendar the location of Easter is simply the first sunday after the first full moon after the first day of spring.

 

Here is a formula that locates the day of the week on which Christmas, December 25th, falls in the years 1600 to 9999.

 

For additional fun you may wish to prove why it only works for those years.

 

 

HOW TO CALCULATE THE DAY OF THE WEEK ON WHICH CHRISTMAS FALLS IN THE CHRISTIAN CALENDAR.

 

 

A way to calculate the day of the week on which Christmas will fall in any year from the year 1600 to the year 9999 in the Christian calendar is as follows.

 

[You can write a simple computer program (in the language of your choice) to do these calculations.]

 

Consider the year ABCD.  Separate the four digits used to express the year into two numbers of two digits each; AB as one number and CD as the other.

 

Let the two digit number AB = C (the century) and let the two digit number CD = Y (the year).

 

Calculate the greatest integer contained in C/4.  Call it R.

Calculate the greatest integer contained in Y/4.  Call it S.

 

Calculate the number Z = 50 + Y + R + S - (2*C)

 

Calculate the remainder when Z is divided by 7.  Call it N.

 

N is the day of the week on which Christmas will fall in that year using the code:

 

0 = Sunday

1 = Monday

2 = Tuesday, etc.

 

FOR EXAMPLE: In the year 1999, Christmas fell on Saturday, so N should equal 6.

 

Thus:  C = 19, Y = 99.  C/4 = 4.75, R = 4.  Y/4 = 24.75, S = 24.

 

Then:  Z = 50 + 99 + 4 + 24 - (2*19) = 139.

 

And:  139 = 19*7 + 6 so N = 6 which codes to Saturday.

 

 

(Remember that there are two types of people in this world.  The first are those who do not do mathematics. The second are those who take care of the first.)

 

Buck

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