Find the number of triangles in the given figure?

                       

The elements move in the sequence the elements reaching the upper-left and the lower-right positions rotate 90 ^oACW; the elements reaching the upper-right and lower-left positions rotate 90 ^oCW; the central element rotates 90 ^oACW and gets laterally inverted.

One arc and four arcs get inverted alternately.

3, 5, 8 have similar designs (four leaves placed close to a small circle and forming a symmetrical design at the centre of the figure).

2, 6, 9 have similar designs (three of the corners of the main figure are shaded black and there is a pattern formed around a '+' sign at the centre of the figure).

1, 4, 7 have similar designs (there are four small circles at(the corners of the main figure and there is a wheel shaped element at the centre of the figure).

In the first step, the ACW end element moves two spaces (each space is equal to half-a-side of the square boundary) in an ACW direction. In the second step, the CW-end element moves three spaces ACW. In the third step, the remaining element moves four spaces ACW. The three steps are repeated to continue the series.

The fig. (X) is similar to Form V. So, when the sheet shown in fig. (X) is folded to form a cube, then the face with shading lies opposite to the free bearing a square, the face bearing a dot lies opposite to a blank face and the face bearing a circle (with a '+' sign inside it) lies opposite to another blank face. The cubes in figures (2) and (4) have the shaded face adjacent to the face bearing a square. Therefore, the cubes in these two figures cannot be formed. Hence, only cubes in figures (1) and (3) can be formed.