A patent attorney has 4 different patents to review, each associated with one of 3 distinct technology sectors. In how many ways can the patents be assigned to sectors such that no sector is left without a patent?

Tue, 05 May 2026 11:38:05 +0000

**Why the Number of Patent Assignments Is Bigger Than Many Realize**
In today’s fast-evolving tech landscape, the allocation of inventions to relevant innovation sectors is more than a bureaucratic formality—it impacts investment, legal strategy, and market positioning. When a patent attorney must assign 4 unique patents across 3 distinct technology sectors, the challenge lies in ensuring each sector receives at least one patent, preventing any gap in coverage. With global innovation accelerating across fields like artificial intelligence, biotech, and cybersecurity, understanding how these assignments work reveals deeper insights into intellectual property management. This multifaceted question—how many ways can 4 different patents be assigned to 3 sectors without leaving a sector empty?—rings with increasing relevance amid growing emphasis on strategic IP portfolios. **Why This Assignment Matters Today**
Across the United States, companies and inventors are navigating a complex web of patent classifications to protect emerging technologies. With competitors racing to secure market advantages, ensuring every sector gets its share from a set of patents supports robust risk mitigation and innovation tracking. The four patents represent distinct breakthroughs, and assigning them to sectors—say machine learning, quantum computing, medical devices, and clean energy—mirrors real-world categorization needed for licensing, collaboration, and legal clarity. Yet without balanced distribution, no single sector dominates unfairly, leaving others underrepresented. This structure ensures balanced exposure and strategic alignment with technological divergence. **How Patent Assignment Works: A Clear Breakdown**
Assigning 4 distinct patents to 3 technology sectors with no sector empty is a combinatorial challenge solved using the principle of inclusion and exclusion, aligned with surjective mappings in set theory. Each patent can go into any of the 3 sectors—3⁴ = 81 total combinations. But not all assignments meet the requirement: we exclude cases where one or more sectors remain empty.