ATDH Perceptual Ability: Cube Counting

Question 1

In ATDH cube-counting items, a stack of identical cubes is painted on every exposed surface. Which surface is never counted as painted?

Accepted Answer

The bottom faces resting on the surface the stack sits on

Answer

Every exposed surface is painted except the bottom of the stack, which rests on the table. Faces covered by a neighbouring cube are also unpainted, but hidden back faces are still painted if nothing touches them.

Question 2

Three cubes sit side by side in a single straight row on a table (1 cube high, 1 cube deep, 3 cubes long). How many cubes have exactly 4 painted sides?

Accepted Answer

2

Answer

Each end cube has its top, front, back and outer end painted, which is 4 sides. Its bottom and the side touching the middle cube are not painted. The middle cube has only 3 painted sides (top, front, back). So 2 cubes have exactly 4.

Question 3

Four cubes form a 2×2 square in a single layer on a table. How many cubes have exactly 3 painted sides?

Accepted Answer

4

Answer

Every cube is a corner cube. Each has its top and two outer side faces painted, which is 3. Its bottom rests on the table and its two inner faces touch neighbours. All 4 cubes have exactly 3 painted sides.

Question 4

Eight cubes form a 2×2×2 block resting on a table. How many cubes have exactly 2 painted sides?

Accepted Answer

4

Answer

Each top-layer cube has 3 painted sides: its top and two outer sides. Each bottom-layer cube has only its two outer sides painted, because its bottom is on the table and its top is covered. That makes 4 cubes with exactly 2.

Question 5

Under ATDH cube-counting rules, what is the maximum number of painted sides any single cube can have?

Accepted Answer

5

Answer

A cube always rests on something, either the table or another cube, so at least its bottom face is unpainted. An isolated cube on the table has 5 painted sides, which is the maximum.

ATDH - Admission Test for Dental Hygiene Practice Test

ATDH - Admission Test for Dental Hygiene Practice Test

ATDH Perceptual Ability: Cube Counting