Question

How does Russell determine the birthdays by examining the numbers? (info in description)

Answer 1

Subtract `205` which will give us last two digits as day and first one or two digits as month.

Explanation:

Let the month be `m` and day be `d`.

First step gives us `5m+7`.

Second step gives us `(5m+7)xx4=20m+28`

Third step gives us `20m+28+13=20m+41`

Fourth step gives us `(20m+41)xx5=100m+205`

and fifth step gives us `100m+205+d`

So first subtract `205` which will give us `100m+d` and we get last two digits as day and first one or two digits gives us month.

In first case for Dave we get `612-205=407`, hence `7^(th)` April, in second case of Ricky, we get `1129-205=924`, hence `24^(th)` September and in the case of Mike, we get `1436-205=1231` i.e. `31^(st)` December.