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📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 Sei $S$ der Gesamtanzahl solcher Zahlen: $2^8 = 256$, da jede Stelle 2 Möglichkeiten hat.

📌 Sei $A$ die Anzahl der 8-stelligen Binärstrings (with digits 2 and 3) that **do not** contain 222 as a substring.

📌 We compute $A$, then subtract from 256:

📌 \text{Answer} = 256 - A

📌 Wir definieren eine Rekursion für die Anzahl der Strings der Länge $n$ über $\{2,3\}$ ohne „222.

📌 Let $a_n$ = number of such strings of length $n$ with no three consecutive 2s.

📌 $a_n = b_n + c_n + d_n$, but easier: define based on how the string ends.

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