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📅 May 13, 2026 👤 scraface

May 13, 2026

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📌 From these, subtract the number with all digits A (i.e., 000A is invalid because it starts with 0). There is only 1 such sequence: 000A.

📌 We need to count the number of 4-digit sequences using both A and B, with the first digit being either A or B.

📌 Total sequences using A and B with all combinations (first digit A or B):

📌 All of these sequences start with A or B (since both digits are nonzero), so no need to exclude sequences starting with 0.

📌 Question: A climate scientist is modeling sea level rise scenarios using binary strings of length 8, where each bit represents a coastal zone either flooded (1) or not flooded (0). How many such strings have at least three consecutive 1s?

📌 Total number of binary strings of length 8:

📌 Let $a_n$ be the number of binary strings of length $n$ with no three consecutive 1s.

📌 If the string ends in 0, the previous $n-1$ bits can be any valid string of length $n-1$.

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