Whole-genome knockout collections are invaluable for connecting gene sequence to function, yet traditionally, their construction has required an extraordinary technical effort. Here we report a method for the construction and purification of a curated whole-genome collection of single-gene transposon disruption mutants termed Knockout Sudoku. Using simple combinatorial pooling, a highly oversampled collection of mutants is condensed into a next-generation sequencing library in a single day, a 30- to 100-fold improvement over prior methods. The identities of the mutants in the collection are then solved by a probabilistic algorithm that uses internal self-consistency within the sequencing data set, followed by rapid algorithmically guided condensation to a minimal representative set of mutants, validation, and curation. Starting from a progenitor collection of 39,918 mutants, we compile a quality-controlled knockout collection of the electroactive microbe Shewanella oneidensis MR-1 containing representatives for 3,667 genes that is functionally validated by high-throughput kinetic measurements of quinone reduction.