2025 IMO Problems/Problem 1
A line in the plane is called sunny if it is not parallel to any of the 
–axis, the 
–axis, or the line 
.
Let 
be a given integer. Determine all nonnegative integers 
such that there exist 
distinct lines in the plane satisfying both of the following:
- For all positive integers
and 
with 
, the point 
lies on at least one of the lines; and - Exactly
of the 
lines are sunny.
and 
with 
, the point 
lies on at least one of the lines; and
Video Solution
https://www.youtube.com/watch?v=kJVQqugw_JI [includes motivational discussion]
