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Home » Distance from $(0,0,0)$: - Upplift

Distance from $(0,0,0)$: - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Question:** In a futuristic city, a transportation system uses pods that can be painted in 5 different colors. If a route requires a sequence of 4 pods, and adjacent pods cannot share the same color, how many valid color sequences exist for the route?

📌 Solution:** For the first pod, there are 5 possible color choices. For each subsequent pod, since it cannot match the previous one, there are 4 choices. Thus, the total number of valid sequences is:

📌 \times 4 \times 4 \times 4 = 5 \times 4^3 = 5 \times 64 = 320

📌 Therefore, the number of valid color sequences is \(\boxed{320}\).

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