Latest How Many Triangles Riddles

There are 20 triangles in the picture.

There are a total of 47 triangles.

Let us divide the triangles in this figure in three equal triangles (triangles formed by connecting outer side to the center of the circle) and then count the number in each category by taking two or more together.

At first, let us count the triangles that are in one part. There are 4 non-overlapping and 3 overlapping triangles. This means that the total triangles are 7 * 3 = 21.

Next, we pick up the triangles by taking two parts together. There are 8 such triangles. 8 * 3 = 24.

Lastly, the triangles by taking all 3 parts together, we find there are only 2 triangles.

21 + 24 + 2 = 47.

38

Let us begin by counting the smallest triangles assuming that they are 1 unit in side. You can find 12 triangles facing upwards (3 + 4 + 3 + 2) and 12 triangles facing downwards.

Now move to the bigger triangle with say side of 2 units. You can find 6 upward facing triangles (3 + 2 + 1) and 6 downward facing triangles.

Next are the biggest triangles with side 3 units (assumingly). You can find 1 upward facing triangle and 1 downward facing triangle.

12 + 12 + 6 + 6 + 1 + 1 = 38

35

64

8

40

16 + (8x2) + (4x2) + (1x2) + (1x2)

20 Triangles

Let us assume that the smallest side of the triangle is 1cms.
Number of triangles with a side of 1 cms = 12
Number of triangles with a side of 2 cms = 6
Number of triangles with a side of 3 cms = 2

Total = 20

13