Cool puzzle taken from a magazine:

"Three children of different ages share the same birthday. On one of their birthdays, one of their ages was the sum of the other two ages. On another birthday a few years later, the youngest observed that one of their ages was half the sum of the other two ages. When the number of years since the first occasion was half the sum of the ages on the first occasion, one celebrated her 18th birthday. What birthdays were the other two celebrating at this time?"