Difference between revisions of "2005 AMC 12A Problems/Problem 25"

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== Problem ==
 
== Problem ==
 
Let <math>S</math> be the set of all points with coordinates <math>(x,y,z)</math>, where x, y, and z are each chosen from the set {0,1,2}. How many equilateral triangles all have their vertices in <math>S</math>?
 
Let <math>S</math> be the set of all points with coordinates <math>(x,y,z)</math>, where x, y, and z are each chosen from the set {0,1,2}. How many equilateral triangles all have their vertices in <math>S</math>?

Revision as of 08:07, 9 September 2007

Problem

Let $S$ be the set of all points with coordinates $(x,y,z)$, where x, y, and z are each chosen from the set {0,1,2}. How many equilateral triangles all have their vertices in $S$?

Solution

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See also