#91
Total no of Triangles ?????
Difficulty Level - 4/5
Total no of Triangles ?????
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Hint :
There are a number of ways to tackle a problem like this; most are equally valid, but some are significantly more reliable than others. The most typical approach for this type of problem is to determine all the possible triangle shapes, and then determine how many of each type there are. The symmetry of this diagram greatly simplifies the task.
My favorite technique counts the triangle not by shape, but by how many of the 6 star vertices are used. The surprising key observation is that there are NO triangles that don't use one of these six points! The diagram's symmetry further reduces the search space, and the counting turns out to be pretty easy.
Hint :
There are a number of ways to tackle a problem like this; most are equally valid, but some are significantly more reliable than others. The most typical approach for this type of problem is to determine all the possible triangle shapes, and then determine how many of each type there are. The symmetry of this diagram greatly simplifies the task.
My favorite technique counts the triangle not by shape, but by how many of the 6 star vertices are used. The surprising key observation is that there are NO triangles that don't use one of these six points! The diagram's symmetry further reduces the search space, and the counting turns out to be pretty easy.
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