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Home » Click Faster: Discover the Ultimate Mouse Polling Rate Change Trick! - Londonproperty

Click Faster: Discover the Ultimate Mouse Polling Rate Change Trick! - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 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**.

📌 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**.

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