A solid cube of 4 inches has been painted red, green and black on pair of opposite faces. It has been cut into one inch cubes. How many cubes have only one face painted?

The elements move downwards along the diagonal and the lowermost element moves to the uppermost position. The triangle and the half shaded rectangle get vertically inverted and the pentagon rotates 90 ^oCW.

The figure may be labelled as shown.

The simplest triangles are AKI, AIL, EKD, LFB, DJC, BJC, DHC and BCG i.e. 8 in number.

The triangles composed of two components each are AKL, ADJ, AJB and DBC i.e. 4 in number.

The triangles composed of the three components each are ADC and ABC i.e. 2 in number.

There is only one triangle i.e. ADB composed of four components.

Thus, there are 8+ 4 + 2 + 1= 15 triangles in the figure.

The line segment along one of the sides of the figure moves two spaces ACW (each space is equal to a side of the figure) and the other element moves three spaces CW.