AMC 8 2020 Problem 9 | Cube Problem

Try this beautiful problem based on cube from AMC 8, 2020.

Cube Problem - AMC 8 2020 Problem 9

Samuel's birthday cake is in the form of a $4 \times 4 \times 4$ inch cube. The cake has icing on the top and the four side faces, and no icing on the bottom. Suppose the cake is cut into 64 smaller cubes, each measuring $1 \times 1 \times 1$ inch, as shown below. How many of the small pieces will have icing on exactly two sides?

12
16
18
20
24

Key Concepts

Game problem

Cube

combination

Suggested Book | Source | Answer

AMC 8 2020 Problem 9

20

Try with Hints

See that, small cube which is in base all the cubes have icing in only one side expect the corner cubes,

Notice the same thing happens for the second and third layer.

For the first layer, only the cubes which are not in corner they have icing in two face.

Cube Problem - AMC 8 2020 Problem 9

Samuel's birthday cake is in the form of a $4 \times 4 \times 4$ inch cube. The cake has icing on the top and the four side faces, and no icing on the bottom. Suppose the cake is cut into 64 smaller cubes, each measuring $1 \times 1 \times 1$ inch, as shown below. How many of the small pieces will have icing on exactly two sides?