\section*{Problem 4 - 061014}

On New Year's Day in 1953, \(A\) and \(B\) met during a train ride. In the course of their conversation, the topic of their ages came up.

\(A\) said: "If you calculate the sum of the digits of my (four-digit) birth year, you will get my age." After a brief moment of thought, \(B\) then congratulated \(A\) on his birthday.

a) How did \(B\) know, without receiving any further information, the birth date?

b) When was \(A\) born?