Information Overview
2025 AIME II Review
The 2025 American Invitational Mathematics Examination II (AIME II) delivered an engaging and challenging set of problems, showcasing the depth of mathematical creativity and problem-solving skills required at this level. Below, we highlight some of the most interesting and unique problems from this year’s exam.
Noteworthy Problems
Problem 3: Grid Coloring Challenge
This problem involved coloring the sides of a 2x2 grid of unit squares with red and blue while following strict constraints. The combinatorial complexity made it an intriguing test of pattern recognition and casework.
Problem 6: Inscribed Rectangle in Tangent Circles
A fascinating geometry problem involving two internally tangent circles and an inscribed rectangle within the smaller one. The symmetry and required area computations added an extra layer of challenge.
Problem 8: The Greedy Coin Algorithm
A number theory and algorithmic problem exploring when the greedy algorithm for coin selection succeeds in minimizing the number of coins used. It required both theoretical insights and systematic case analysis.
Problem 14: The Equilateral Triangle Puzzle
This problem presented an unexpected geometric construction inside a right triangle, where distances between key points were all equal. The challenge of finding the area of an embedded quadrilateral was particularly rewarding.
Overall Impressions
The 2025 AIME II was well-balanced, with a mix of algebra, number theory, combinatorics, and geometry problems. It tested both computational accuracy and deep mathematical thinking. The inclusion of unique geometric constructions and algorithmic challenges made it a memorable competition.