JMO 1993 Problem 3

$x$ students took an exam with $y$ problems. Each student solved a half of the problem and the number of person those who solved the problem is equal for each problem.For any two students exactly three problems could be solved by the two persons. Find all pairs of $(x,\ y)$ satisfying this condition, then show an example to prove that it is possiible the case in terms of $a,\ b$ as follows: Note that every student solve $(a)$ or don't solve $(b)$.