Mathematical Problem 4: Solution

This is the solution to the problem set on 9 April.

We observed that if a daughter is born in '66 and her mother in '44 then in the year that the mother turns 66, the daughter turns 44.

Was this an unusual coincidence? Of course not! It happens for any two people! It would be fun to try this as a little investigation with some primary school children.

For example, if A was born in 1957 and B was born in 1971, then in the year that A turns 71 B turns 57. Why? Because the age of A minus the age of B (once they have both had their birthdays) is always equal to the birth year of B minus the birth year of A. If A is born 14 years earlier than B then B is always 14 years younger than A. So when A's age equals B's birth year (ignoring the 1900) then B's age (14 less than this) must equal A's birth year.

Why had I never noticed that before?!

There is a complication if they are born in different centuries, – this requires the older person to pass 100 before the phenomenon occurs. For example, Catherine was born in 1966 and her son, Jack, was born in 2001. So, the year Jack turns 66, Catherine will turn 101!