# Method in Determining Calendar Dates

What day will the Christmas day fall 50 years from now? What day of the week is your birthday? Isn’t it fascinating to answer that question accurately? In this post I will share a way to make it possible.  You will be stunned that determining the answers to such questions is just a matter of substitution.

Before we start, let me introduce some tools that we need.

Integer Division – a division that is only taking the integer part of the quotient.

Example:      $\displaystyle\frac{25}{7}=3$

Modulo Division – a division that is taking the remainder as the answer and not the quotient.

Example:     $25mod7=4$, the same thing if we say the remainder of 25 when divide by 7 is 4.

Note: all division that will be used here is strictly integer division unless specified.

Formula in determining the day of the week a certain date falls.

Step 1: Solve for A,Y and M

$A=\displaystyle\frac{14-Months}{12}$

Months in number( January=1, February=2,March=3,etc.)

$Y= Year-A$

$M=Months+12A-2$

$d=(day+Y+\displaystyle\frac{Y}{4} - \displaystyle\frac{Y}{100}+\displaystyle\frac{Y}{400}+\displaystyle\frac{31M}{12})mod7$

day- is the specific date, Y- year

d-is the day of the week

0= Sunday

1=Monday

2=Tuesday

3=Wednesday

4=Thursday

5=Friday

6=Saturday

Sample Problem 1:

What day of the week does November 25, 2013 have fallen?

Solution:

Solve for A:  Months=11(November)

$A=\displaystyle\frac{14-11}{12}$

$A=0$

Solve for Y:

$Y= Year-A$

$Y= 2013-0$

$Y= 2013$

Solve for M:

$M=11+12(0)-2$

$M=9$

Solve for d:

$d=(25+2013+\displaystyle\frac{2013}{4} - \displaystyle\frac{2013}{100}+\displaystyle\frac{2013}{400}+\displaystyle\frac{31(9)}{12})mod7$

$d=(25+2013+503-20+5+23)mod7$

$d=2549mod7$

$d=1mod7$ , meaning that d=1, 1=Monday. I have chosen the date so that you can check your calendar that it is really correct.

Sample Problem 2:

What day will the Christmas day fall 50 years from now?

Solution:

The date will be December 25,2063.

Solve for A:

$A=\displaystyle\frac{14-12}{12}$

$A=0$

Solve for Y:

$Y= Year-A$

$Y= 2063-0$

$Y= 2063$

Solve for M:

$M=12+12(0)-2$

$M=10$

Solve for d:

$d=(25+2063+\displaystyle\frac{2063}{4} - \displaystyle\frac{2063}{100}+\displaystyle\frac{2063}{400}+\displaystyle\frac{31(10)}{12})mod7$

$d=(25+2063+515-20+5+25)mod7$

$d=2613mod7$

$d=2mod7$, or d=2 and that is Tuesday.

Now try to check what day you were born.

Practice Problem:

1. What day of the week does December 7, 1945 have fallen?

2. World War 1 started July 28, 1914. What day of the week was it?

3. Little Boy is the name of the atomic bomb dropped in Hiroshima, Japan on August 6, 1945. What day of the week that happened?

4. Marie Skłodowska-Curie is the real name of Polish Marie Curie, the first woman who won Nobel Prize in both Chemistry and Physics with her work in radioactivity. She was born on November 7,1867. What day was that?

5. I was born September 22, 1989. What day of the week does that fallen?