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Sign Pyramid – AMC 8 2018 Problem 19

In a counting problem, you may need to stabilize the number of cases. This means, by letting some of the variables change, one may fix the remaining cases.

This is the central idea in the following problem from American Mathematical Contest 8 (AMC 8, 2018, Problem 9).

Paper Folding Geometry – AMC 10

We fold a paper using GeoGebra and explore a problem from American Mathematical Contest (AMC 10)

Integers in a Triangle – AMC 10A

There is an intuitive definition of perpendicularity. It does not involve angle. Instead, it involves the notion of distance. Consider a point P and a line L not passing through it. If you wish to walk from P to L, the path of shortest distance is the perpendicular drawn from P to L.