So after placing 3 non-adjacent C’s (20 ways), we have 5 remaining positions to place 2 A’s and 3 G’s, with **no two A’s adjacent** and **no two G’s adjacent**.

Thu, 30 Apr 2026 13:59:36 +0000

Mastering Non-Adjacent Placement: Arranging 3 Non-Adjacent C’s, 2 A’s, and 3 G’s with Strict Adjacency Rules Creating balanced and valid sequences in permutation-based puzzles often involves strict spacing rules. In this challenge, after placing 3 non-adjacent C’s in a string of 10 total positions, you’re left with 5 free positions to fill with 2 A’s and 3 G’s—under the critical constraint that no two A’s may be adjacent, and no two G’s can be adjacent either. This article breaks down how to solve this combinatorial problem efficiently, with 20 foundational strategies and 5 advanced optimizations to ensure valid arrangements. --- ### Understanding the Constraints