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Home » Clean tubes: \( 150 - 105 = 45 \) - Groen Casting

Clean tubes: \( 150 - 105 = 45 \) - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 However, due to the complexity and size, we apply a known combinatorial method: **counting valid permutations with forbidden adjacency** using inclusion-exclusion or generating functions — but a more efficient way is to use **placement algorithms**.

📌 Alternatively, we proceed by **constructing valid sequences** using dynamic programming or recursive counting, but for Olympiad-style reasoning, we can use the **principle of arranging with separation**.

📌 But here’s a better and feasible approach:

📌 We use **inclusion-exclusion over forbidden adjacents**, but that becomes intractable due to multiple overlapping cases.

📌 Instead, we use a **constructive counting method** with **placement strategy**.

📌 Let’s consider that we are placing 8 positions, assigning A, C, G with multiplicities 2, 3, 3, such that **no two identical letters are adjacent**.

📌 We proceed in steps:

📌 First, place the most frequent letters: C and G (both appear 3 times). Since no two C’s or G’s can be adjacent, we must ensure they are separated.

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