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Home » Check that \(x = \sqrt5 y\): - GetMeFoodie

Check that \(x = \sqrt5 y\): - GetMeFoodie

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 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.

📌 But we cannot place all three C’s without adjacency unless separated by at least one non-C.

📌 Similarly for G.

📌 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**.

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