AMC 8 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 3 Medium

4 colors are available (not necessary to use all) to paint each part of the figure below. If the colors in adjacent parts cannot be the same, how many ways of painting are there?

  • A.

    144

  • B.

    288

  • C.

    72

  • D.

    36

  • E.

    6

Answer:C

Case analysis:

First fill the middle part, which has 4 possibilities.

(1) AC has the same color:

4 \times 3 \times 1 \times 2 \times 2 = 48

(2) AC has different colors:

4 \times 3 \times 2 \times 1 \times 1 = 24

Thus,

48 + 24 = 72~\text{ways}.

Therefore, the answer is: \text{C}.

Related Problems
Problem 1 AMC 8 Daily Practice Round 1
Problem 2 AMC 8 Daily Practice Round 1
Problem 4 AMC 8 Daily Practice Round 1
Problem 5 AMC 8 Daily Practice Round 1
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