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Tag Archives: optimization
Conceptual Solution to 2008 AIME I, Problem 14
Here’s a solution to problem 14 on the 2008 AIME I contest that attempts to avoid computation as much as possible. Sometimes, it’s an amusing exercise to try to solve a contest problem entirely in your head. Doing so often forces … Continue reading
Posted in Contest Math, math
Tagged AIME, circles, ellipse, geometry, optimization, tangent
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2013 AIME 2 Problem 10
I’ve been asked about the following problem from the 2013 AIME 2 a few times, so I decided to blog a couple of solutions for it: Given a circle of radius , let A be a point at a distance from … Continue reading
Bouncing in a UShaped Gallery
Consider the Ushaped hallway illustrated above. All angles are right angles and the numbers indicate the lengths of various walls. The figure is not drawn to scale. The problem is to send a point sized billiard ball located at the … Continue reading
Two Lady Bug Path Problems
The other day, I noticed a bunch of lady bugs walking in the grooves of a tiled floor.
Posted in math, Math Education
Tagged distance, geometry, optimization, paths, taxicab metric
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Greedy Clams – Solution
Here’s a solution to the Greedy Clam problem that was inspired by Luyi’s “Satiated Clam” geometry problem.
Greedy Clams
Here’s a problem inspired by Luyi’s “Satiated Clam” problem. (Her problem makes me think of a clam with the biggest possible pearl inside.) The problem begins with the same setup as hers. Let ABCDEF and ABC’D’E’F’ be two regular hexagons with unit … Continue reading