Bay Area Mathematical Olympiad #0kxj
Bay Area Mathematical OlympiadHard
From module Shoelace Theorem II
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Understand the scale
Scale
0.5: Easiest math competition problems, often solvable even for early middle school students without experience.
1: Problems strictly for beginners, often at a moderate middle school level.
1.5: Problems for stronger beginner students, on the level of the middling problems in most middle school contests.
2: For motivated beginners, harder questions from the previous categories.
2.5: More advanced beginner problems, hardest questions from previous categories.
3: Early intermediate problems that require more creative thinking.
3.5: Tougher early intermediate problems that consistently stretch into higher-level creative thinking or conceptual knowledge.
4: Intermediate-level problems.
4.5: Upper intermediate problems approaching the upper bound for non-invitational sprint math competitions.
5: More difficult AIME problems or simple proof-based Olympiad-style problems.
6: High-level AIME-styled questions or introductory Olympiad-level questions.
7: Tougher Olympiad-level questions, may require more technical knowledge.
8: High-level Olympiad-level questions.
9: Expert Olympiad-level questions.
9.5: The hardest problems appearing on Olympiads which the strongest students could reasonably solve.
10: Historically notorious problems, generally unsuitable for even very hard competitions because they are exceedingly tedious, long, and difficult.
Pick's theoremVectorsDeterminantsTriangle centers: centroid, incenter, circumcenter, orthocenter, Euler line, nine-point circleModular Arithmetic
Problem
Problem:
A lattice point in the plane is a point with integer coordinates. Let be a triangle in the plane whose vertices are lattice points, but with no other lattice points on its sides. Furthermore, suppose contains exactly four lattice points in its interior. Prove that these four points lie on a straight line.