## How to Guess the Day of the Week Your Friend Was Born

If you have some friends born between 1900 and 2000, then maybe you can impress them with this trick: find the day of the week that they were born.

Here are the steps:

(1) Let $y$ be the year of their birth. Evaluate $\frac{y - 1}{4}$ and ignore the remainder. For example, we want to know the date March 3, 1947, then we have

$\displaystyle \frac{1947 - 1}{4} = \frac{1946}{4} = 486$.

(2) Find what day of the year is the date and let’s represent it D. There are 31 days in January, 28 days in February, and March 3 is the third day.

$D = 31 + 28 + 3 = 62$

(3) Let $s = y$ + the result in (1) + $D$.

$s = 1947 + 486 + 62 = 2495$

4.) Divide $s$ by $7$ and get the remainder.

$\frac{2495}{7} = 356$ remainder $3$.

Now, you can guess the day of the week using the remainder.

Remainder: Day

0: Friday
1: Saturday
2: Sunday
3: Monday
4: Tuesday
5: Wednesday
6: Thursday

Hence, March 3, 1947 is a Monday.

Source: Nature of Mathematics