Cubes & dice aptitude

Question 1

A cube painted red on all faces is cut into 64 identical smaller cubes. How many small cubes have exactly two faces painted?

Accepted Answer

24

Answer

16

Answer

8

Answer

32

Question 2

A cube painted on all faces is cut into 64 identical smaller cubes. How many small cubes have no face painted?

Accepted Answer

8

Answer

16

Answer

24

Answer

0

Question 3

A cube painted on all faces is cut into 125 identical smaller cubes. How many small cubes have exactly one face painted?

Accepted Answer

54

Answer

36

Answer

48

Answer

60

Question 4

A cube painted on all faces is cut into 27 identical smaller cubes. How many small cubes have at least one face painted?

Accepted Answer

26

Answer

20

Answer

24

Answer

27

Question 5

A cuboid measuring 4 cm × 3 cm × 2 cm is painted on all faces and cut into 1 cm cubes. How many of these cubes have exactly two faces painted?

Accepted Answer

12

Answer

8

Answer

16

Answer

4

Question 6

Two positions of the same die are described as (top, front, right). Position 1: top 1, front 2, right 3. Position 2: top 1, front 3, right 5. Which number is opposite 2?

Accepted Answer

5

Answer

3

Answer

4

Answer

6

Question 7

A die numbered 1 to 6 is rolled several times. Across these throws, the faces seen next to (adjacent to) the face showing 1 were 2, 3, 4 and 5. Which number is on the face opposite 1?

Accepted Answer

6

Answer

2

Answer

5

Answer

Cannot be determined

Question 8

On a standard die, opposite faces add up to 7. The die rests on a table with 5 on top. What is the sum of the numbers on its four side faces?

Accepted Answer

14

Answer

16

Answer

12

Answer

15