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How many triangles #4

(1 votes, average: 1.00 out of 5)

January 14, 2013 by puzzler 1 Comment

1.) How many triangles do you see in this image ?

how many triangles do you see  in this image

how many triangles do you see in this image

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Answer with Solution

Looking at the symmetry, we can divide this triangle in 5 equal parts(square) and we will first count the number of triangles in each part and then number of triangles formed by combining 2 or more parts together.
Number of triangles in one square: 8(non overlapping triangles) + 8(overlapping triangles with middle lines a part of the triangle) =16*5 = 80
Number of triangles by taking two squares(one middle and one other) at a time: 4*4(there are four such combinations) = 16
Number of triangles by taking (only) three squares(one middle and two others) at a time: 4(all squares should be a part of the triangle) *4(four such combinations) = 16
Number of triangles by taking 4 squares together: 2 *4(four such combinations) = 8

Thus total number of triangles = 80 + 16 + 16 + 8 = 120.

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Comments

  1. Jack says

    February 26, 2015 at 7:03 am

    Are you sure you are not double counting?

    Reply

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