1999 JBMO Problems/Problem 3
Revision as of 11:50, 12 August 2020 by Duck master (talk | contribs) (created page w/ solution & categorization)
Let be a square with the side length 20 and let be the set of points formed with the vertices of and another 1999 points lying inside . Prove that there exists a triangle with vertices in and with area at most equal with .
Triangulate into triangles with vertices being the vertices of and the members of . There are triangles thusly formed, so by the pigeonhole principle, at least one of the holes has to have area at most , and we are done.
|1999 JBMO (Problems • Resources)|
|1 • 2 • 3 • 4 • 5|
|All JBMO Problems and Solutions|