Proven Jigsaw Sudoku

Jigsaw sudoku replaces the familiar three-by-three boxes of ordinary sudoku with irregular nine-cell regions that snake across the grid like puzzle pieces. Row and column constraints remain â " each row and column still contains the digits one through nine exactly once â " but the box constraint is now interpreted over the irregular shapes. The variant is sometimes called "squiggly sudoku" or "geometric sudoku," but "jigsaw" captures the feel of solving one most accurately: your eye, trained over years to snap to three-by-three blocks, must learn to trace region boundaries that meander. The initial adjustment is perceptual more than logical. A few puzzles in, you will begin to see that irregular regions actually provide more cross-elimination opportunities than standard boxes, because a jigsaw region can span more rows and more columns than a three-by-three square ever could. A region that spans four different rows constrains four rows at once; a region that spans five different columns constrains five columns at once. The reasoning you develop in jigsaw sudoku carries over to ordinary sudoku and makes you a better solver of the standard variant as well. This book contains 200 jigsaw puzzles, every one generated by our constraint-satisfaction engine and verified by exhaustive backtracking to have exactly one solution. The difficulty range runs from genuinely easy introductions â " suitable for a reader who has never attempted a jigsaw grid before â " through expert puzzles that exploit the extra reach of irregular regions in ways that are impossible in standard sudoku. At the expert end, some puzzles use regions that span seven or eight different rows, which is impossible in a standard sudoku box and which creates long chains of row-based elimination that no ordinary sudoku technique can match. Each puzzle carries a cryptographic hash under its answer grid so the puzzleâ "solution pair can be independently verified. The classic jigsaw technique that surprises readers new to the variant is "law of leftovers" if you take any set of whole rows and then subtract the jigsaw regions that fall entirely within those rows, the remaining cells form a set that must contain a specific multiset of digits. This is the jigsaw cousin of the Rule of 45 from killer sudoku, and it is the most powerful single technique in the variant. The rules page at the front of this book introduces law of leftovers with a worked example, and the first several puzzles in the gentle section are designed to exercise it. None of the puzzles in this collection require guessing. Every one is solvable by pure logical deduction. That is the guarantee we make on every title in the Proven Puzzles line, and it is backed by a verification pipeline that rejects any grid that admits zero or multiple solutions. The puzzles that reached this book are the ones our solver signed off on, and the SHA-256 hash under every answer grid lets you confirm it. 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; it discusses jigsaw technique with an emphasis on why the extra rows and columns that irregular regions span are your friend rather than your enemy. Contents: Publisher's Note on the verification process, Euler AI's Editor's Note on jigsaw technique, rules page with worked law-of-leftovers example, 200 verified puzzles arranged from approachable through expert, complete answer key with verification line for every grid, methodology section, and production notes. Typeset in Avenir Next on 70 lb bright white paper; perfect bound; 6 x 9 inches.