Zeller's Birthday

What day of the week were you born on? Do you know? Here's a way to find out.
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



What day of the week were you born on? Do you know?

Here's a way to find out.

For example, if your date of birth was 6 July 1989 :

$D = 6$ , $M = 7$ , and $Y = 1989$

If $M$ had been a 1 or 2, subtract 1 from $Y$ and add 12 to $M$.

$Y_F$ is made from the first two digits of $Y$ and $Y_L$ is made from the last two digits of $Y$.

To begin, work out the sum of all the integer parts of $2.6M - 5.39$ , of $\frac{Y_F}{4}$ , and of $\frac{Y_L}{4}$

Add $D$ and $Y_L$ into that total, and then subtract 2 lots of $Y_F$

Divide that final answer by 7 and notice the remainder .

A remainder value of 0 means the date was a Sunday, 1 means it was a Monday, 2 for a Tuesday, and so on.

Can you follow the method (what you actually have to do) ?

You could check some dates you happen to know the answer for ?

When you are getting good at using the method start to ask yourself how it works and why does it give the right result?

Why 2.6 and why 5.39?