PART 5 (For questions 1 through 15)Several stacks of cubes have been cemented together to form an entire figure. After being cemented, each cube was varnished on all external surfaces (excluding the bottom). The only hidden cubes are those required to support other cubes.You must determine the number of cubes in the figure that have a particular number of varnished sides.
*only one of their sides painted
*only two of their sides painted
*only three of their sides painted
*only four of their sides painted
*all five of their sides painted
Note: There are no problems for which zero (0) is the correct answer.There are five possible answer choices for this PAT section.Here are the rules:

  1. Identical, regular cubes have been used to construct the figure.
  2. The figure’s bottom (the face on which it rests) has not been varnished.
  3. The only possible hidden cubes are those that are necessary to support other visible cubes in the figure. This means that an empty top level implies an entirely empty column when that column is completely out of view.
  4. It is impossible for a cube to have six varnished surfaces.

Try the following example: In this figure, how many cubes have two of their exposed sides painted?

CC_Instructions
There are four cubes in the figure: three are visible and one supporting the top cube that is invisible. The invisible cube has only two sides painted. The top cube has five sides painted. The remaining two cubes have four sides painted.

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