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 be the year of their birth. Evaluate and ignore the remainder. For example, we want to know the date March 3, 1947, then we have

.

(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.

(3) Let + the result in (1) + .

4.) Divide by and get the remainder.

remainder .

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 *