Explanation
Step 1: Color the Central Triangle (Tc)
The central triangle is adjacent to all three corner triangles.
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We have 3 choices for Tc (Red, Blue, or Green).
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Let's assume we pick one color for Tc.
Step 2: Color the Corner Triangles (T1,T2,T3)
According to the condition, no two adjacent regions can have the same color. Since each corner triangle (T1,T2,T3) is adjacent to the central triangle (Tc), they cannot be the same color as Tc.
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For each corner triangle, we have only 2 remaining choices (the colors that were not used for Tc).
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Since the corner triangles are not adjacent to each other (they only touch at a single vertex, not an edge), their color choices are independent of one another.
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Choices for T1: 2 ways
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Choices for T2: 2 ways
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Choices for T3: 2 ways
Step 3: Total Calculation
Using the fundamental principle of counting, we multiply the number of choices for each region:
Total Ways=(Choices for Tc)×(Choices for T1)×(Choices for T2)×(Choices for T3)
Final Answer:
There are 24 ways to color the diagram.
