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Home » Another approach: in a gear train, rotations are conserved per minute of time. - Crankk.io

Another approach: in a gear train, rotations are conserved per minute of time. - Crankk.io

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \(a_6 = a_5 + a_4 = 13 + 8 = 21\)

📌 Thus, number of sequences **with at least one pair of consecutive A’s** is:

📌 \(64 - 21 = 43\)

📌 So the answer is \(\boxed{43}\)

📌 An anthropologist observes a community where 5 distinct rituals are performed in a sequence during a festival. If two specific rituals (say R1 and R2) cannot occur consecutively, how many valid performance orders are possible?

📌 Total number of unrestricted arrangements of 5 distinct rituals: \(5! = 120\)

📌 Now subtract the number of arrangements where R1 and R2 are consecutive.

📌 Treat R1 and R2 as a single block. Then we have 4 units to permute: the block and the other 3 rituals.

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