Problem 1. A line in the plane is called sunny if it is not parallel to any of the x –axis, the y –axis, or the line x + y = 0 .
Let n ≥ 3 be a given integer. Determine all nonnegative integers k such that there exist n distinct lines in the plane satisfying both of the following:
- for all positive integers a and b with a + b ≤ n + 1 , the point (a, b) lies on at least one of the lines; and
- exactly k of the n lines are sunny.
