# 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

## 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 U-Shaped Gallery

Consider the U-shaped 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.

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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.

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## 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

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