Casework & Complementary · Difficulty 5/10 · ~40 min
Casework & Complementary Counting
- Partition into exhaustive, disjoint cases
- Recognize when complementary counting wins
- Combine casework with the product rule
When a counting problem resists a single clean construction, you split it. Casework is controlled demolition: break the problem into pieces you *can* count, then reassemble. The craft lies in choosing cases that are exhaustive, disjoint, and few.