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How many triangles in the large triangle?

Updated: 4/28/2022
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13y ago

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If you are talking about the common triangle puzzle, then there are 27 triangles. There are 16 one-cell triangles, 7 four-cell triangles, 3 nine-cell triangles, and 1 sixteen-cell triangle.

There is a link to the pic for you also.

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The answer in a two dimensional way would be 27. However, if you take into account that each triangle can be turned three ways, then you can understand that there are actually 81 triangles in all.

THen you could ask the question, how many triangles can fit in this space (i.e. the picture)? The answer is the first level of infinitely many, or Aleph zero. This would be by finding the midpoint of each side of the all the 1- cell triangles and creating a new triangle.

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