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2025 AMC 10B Problem 21

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2025 AMC 10B Problem 21AMC 10 Step by Step
Name:                             Date: September 13, 2026
Arrangements with Restrictions · difficulty 5 of 5 · about 12 min · position P21-25

Each of the 99 squares in a 3×33 \times 3 grid is to be colored red, blue, or yellow in such a way that each red square shares an edge with at least one blue square, each blue square shares an edge with at least one yellow square, and each yellow square shares an edge with at least one red square. Colorings that can be obtained from one another by rotations and/or reflections are to be considered the same. How many different colorings are possible?

  1. A)

    33

  2. B)

    99

  3. C)

    1212

  4. D)

    1818

  5. E)

    2727

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