2022 AMC 10 A

Complete problem set with solutions and individual problem pages

Problem 9 Easy

A rectangle is partitioned into 5 regions as shown. Each region is to be painted a solid color - red, orange, yellow, blue, or green - so that regions that touch are painted different colors, and colors can be used more than once. How many different colorings are possible?

  • A.

    120

  • B.

    270

  • C.

    360

  • D.

    540

  • E.

    720

Answer:D

D is special as it touches all the other rectangles.

Step 1: Paint D first, we have 5 choices;

Step 2: Paint C, we have 4 choices;

Step 3: Paint E, we have 5 choices (it's different from D);

Step 4: Paint A and B at last, we have 3 choices for each.

Total number of ways =5\times4\times3\times3\times3=540.

Related Problems
Problem 7 2022 AMC 10 A
Problem 8 2022 AMC 10 A
Problem 10 2022 AMC 10 A
Problem 11 2022 AMC 10 A
Think Academy Powered by ChatGPT