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📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 Question: A science fiction writer is designing a futuristic calendar for a planet orbiting a binary star system. The planet has a unique time cycle where a tide week consists of 7 days, and every 4th tide week forms a storm week with intensified weather. If a tide week begins on day 1, on which day number does the 10th storm week begin?

📌 The first storm week begins on day 28. The second on day 56, the third on day 84, and so on. This forms an arithmetic sequence with first term $ a = 28 $ and common difference $ d = 28 $.

📌 We want the day number of the 10th storm week:

📌 The sequence is arithmetic with first term $ a = 5 $ and common difference $ d = 6 $. The total number of doses after $ n $ days is the sum of the first $ n $ terms:

📌 We want the smallest $ n $ such that:

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