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Home » Wait — 720 minutes in an hour? No. - ClickBalance

Wait — 720 minutes in an hour? No. - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 A glaciologist is tracking the movement of a glacier and records the position of a specific marker every hour. Over a 10-hour period, each position is noted as either advancing (A) or retreating (R). How many sequences of these 10 positions have exactly 6 advances, with no three consecutive advances?

📌 To solve this problem, we need to count sequences of length 10 with exactly 6 advances (A) and 4 retreats (R), with the condition that no three consecutive advances occur.

📌 Lets denote a sequence of advances and retreats as a binary string of length 10, where A is 1 and R is 0, with exactly six As, and no three consecutive As.

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