Proven Samurai Sudoku

Samurai sudoku is the pentagonal variant of ordinary sudoku: five nine-by-nine grids arranged so that four outer grids share their corner three-by-three boxes with a central fifth grid. The resulting figure â " 369 cells in total â " looks at first glance like five independent sudoku puzzles stapled together, but the shared corner regions are what make the variant interesting. A digit placed in one of the overlap boxes must simultaneously satisfy the row, column, and box constraints of two entire grids. The overlap regions are therefore the most constrained parts of the puzzle, and experienced samurai solvers attack them first. This book contains 100 samurai puzzles, every one generated and verified by the Proven Puzzles pipeline. Each of the five constituent grids was checked for uniqueness, and the whole figure was verified as a single coherent puzzle whose solution is mathematically unique. The difficulty range runs from approachable to expert. The gentler puzzles introduce cross-grid reasoning gradually; the hardest ones demand that you hold partial solutions to two grids in your head simultaneously while you work the shared boxes. At the expert end, a single placed digit in an overlap box can cascade through two grids, unlocking cells that no single-grid technique could have reached. No samurai puzzle in this book requires guessing. Every one yields to pure logical deduction â " this is the guarantee that the Proven Puzzles verification pipeline makes on every title in the line. The verification engine is not a heuristic; it is an exhaustive backtracking solver whose only function is to attempt to find a second solution to a puzzle. If it finds one, the puzzle is rejected. If it finds none, the puzzle is certified as unique, and its puzzleâ "solution pair is hashed together with SHA-256 to produce a cryptographic signature. The first twelve characters of that hash are printed beneath the answer grid in the back of this book, so you can verify, independently of us, that the puzzle in your hand is the one the engine signed off on. Samurai sudoku is a solver's variant. It rewards patience above technique; it rewards systematic scanning above intuition; it rewards the willingness to put a partial solution aside, work another grid, and return to the first when new information appears. Readers who enjoy taking their time with a big puzzle over several sittings will find that each samurai grid in this book can comfortably absorb an hour or more of careful work, and some of the expert puzzles may span several sittings. To make the grids easier on the eyes, every samurai puzzle in this book is printed one per two-page spread, with generous margins and large cells. The Editor's Note in this volume is signed by our Euler AI persona â " an artificial mind trained upon the letters and treatises of Leonhard Euler (1707â "1783), speaking here in a modern English rendering of that voice. Euler's own contributions to the combinatorics of Latin squares are the direct ancestor of the sudoku grid; his note here discusses samurai strategy in the spirit of his historical approach to constrained-combinatorial problems, with an emphasis on why the most constrained part of any such problem (in samurai, the shared corner boxes) is always the correct place to begin. Contents: Publisher's Note, Euler AI's Editor's Note on samurai solving strategy, rules page, 100 verified puzzles printed one per two-page spread for legibility, a complete answer key with verification line for every grid, verification methodology, and production notes. Typeset in Avenir Next on 70 lb bright white paper; perfect bound; 6 x 9 inches.