My grandfather, my father, my son and I gathered on 1st April 2006, for a family reunion.

We were all born on the same date and month. We were each born on a Sunday, but not just any Sunday. In each case it was the fifth Sunday of the month.

If I told you the month our common birthday is in, then you'd be able to determine our ages.

In what year was each of us born?

Trevor is correct.

The calendar cycle repeats every 28 years.  A fifth Sunday can occur in any month that has 29+ days.  As each month, except February, has 30 or 31 days, there are two or three days in which the fifth Sunday can occur more than once during the cycle.  As there are seven days in a week, a fifth Sunday occurs four times for each 29th, 30th and 31st that occurs in the month during the 28-year calendar cycle.  Only the month of February, when the leap day is added only every fourth year, is the fifth Sunday not a frequent occurance.  

As pointed out by Trevor, only four Sunday February 29ths have occured in the last 100 years.  If given that the grandfather is not over 100 years old...
your grandfather is age 86 (born February 29, 1920);
your father is age 58 (born February 29, 1948);
you are age 30 (born February 29, 1976); and,
your son is age 2 (born February 29, 2004).   

Edited on July 1, 2006, 8:08 am

Posted by Dej Mar on 2006-07-01 02:30:00