2025 IMO Problems/Problem 1
Revision as of 02:56, 15 July 2025 by Renrenthehamster (talk | contribs) (Created page with "A line in the plane is called <math>sunny</math> if it is not parallel to any of the <math>x</math>–axis, the <math>y</math>–axis, or the line <math>x+y=0</math>. Let <ma...")
A line in the plane is called 
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.
Video Solution
https://www.youtube.com/watch?v=kJVQqugw_JI [includes motivational discussion]
