Thus, the number of valid frequency assignments is $ \boxed{1806} $.

Sun, 03 May 2026 17:06:48 +0000

Title: How Many Valid Frequency Assignments Are There? A Deep Dive Into a Key Combinatorics Problem—Result: $ oxed{1806} $ --- Introduction In the realm of signal processing, telecommunications, and wireless communications, efficient frequency assignment is crucial to avoid interference and maximize spectrum utilization. A fundamental question arises: How many valid frequency assignments satisfy specific constraints? Recent combinatorial investigations reveal a striking result—exactly $ oxed{1806} $ valid frequency assignments exist under a constrained model. This figure emerges from a rich interplay of graph theory, integer programming, and combinatorial optimization. In this article, we unpack the problem, explore its significance, and celebrate this elegant solution of 1806.