Knockout Sudoku is a method for the construction of whole-genome knockout collections for a wide range of microorganisms with as little as 3 weeks of dedicated labor and at a cost of ∼$10,000 for a collection for a single organism. The method uses manual 4D combinatorial pooling, next-generation sequencing, and a Bayesian inference algorithm to rapidly process and then accurately annotate the extremely large progenitor transposon insertion mutant collections needed to achieve saturating coverage of complex microbial genomes. This method is ∼100× faster and 30× lower in cost than the next comparable method (In-seq) for annotating transposon mutant collections by combinatorial pooling and next-generation sequencing. This method facilitates the rapid, algorithmically guided condensation and curation of the progenitor collection into a high-quality, nonredundant collection that is suitable for rapid genetic screening and gene discovery.