A classic children's toy consists of 13 different blocks that combine to form a rectangle showing a man's face. Each block has four sides with alternatives for that part of the face; for example, the block for the right eye might have a closed eye on one side, a partially open eye on another, and so on. A child can turn any block and so change that part of the face, and in this way many different faces can be formed.

How many different faces can be formed by the children's toy?

Question

Mathematics

Desmond Mccall

25 July, 22:28

A classic children's toy consists of 13 different blocks that combine to form a rectangle showing a man's face. Each block has four sides with alternatives for that part of the face; for example, the block for the right eye might have a closed eye on one side, a partially open eye on another, and so on. A child can turn any block and so change that part of the face, and in this way many different faces can be formed.

How many different faces can be formed by the children's toy?

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Answers (1)

Know the Answer?

Phoebe Clay · Answer 1

Answer: 67,108,863 combinations.

Step-by-step explanation:

We have 13 blocks.

Each block has 4 differet options.

The total number of combinations is equal to the product of the options for each variable (the variables are the 13 blocks) so we have that the number of combinations is:

C = 4*4*4*4*4*4*4*4*4*4*4*4*4 = 4^13 = 67,108,863