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Home » | Number seasons = 5 (including repeated runs) - Baxtercollege

| Number seasons = 5 (including repeated runs) - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 A powerful method is to **first arrange the non-C letters**, then insert C’s in safe positions, and similarly for G’s — but since both C and G have 3 copies and adjacency restrictions, and overlap is possible, we need a more systematic way.

📌 Let’s use the **inclusion of gap methods** with all constraints.

📌 Alternate Insight:

📌 Let’s define the total number of permutations of the multiset {A², C³, G³} with **no two identical adjacent letters**.

📌 This is a classic problem in combinatorics on words. A known technique is to use **recursive counting with states**, but we can estimate via careful case analysis.

📌 However, for Olympiad efficiency, we use **the principle of derangement-like placement**.

📌 But instead, let’s use **generating functions with exclusion**, or a **reduced method**.

📌 Better idea: Use **inclusion-exclusion over the number of adjacent pairs**, but again, too broad.

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