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

See Answer### 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**

Jack says

Are you sure you are not double counting?