euler ai (60 resultados)

PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000.

PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000.

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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000.

PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000.

Condición: New.

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Paperback. Condición: new. Paperback. Arrow sudoku adds arithmetic and spatial reasoning to the ordinary sudoku grid in a single elegant rule: each arrow in the puzzle consists of a circle and a directed path of cells, and the digit in the circle equals the sum of the digits along the arrow. From that one rule an entire solving vocabulary emerges. The range of possible circle values is determined by the arrow's length. A two-cell arrow circle must equal the sum of two distinct digits, so it falls between three (1 + 2) and seventeen (8 + 9) a " but since it is a single digit, it must fall between three and nine. A three-cell arrow circle must equal the sum of three distinct digits, so it falls between six (1 + 2 + 3) and twenty-four (7 + 8 + 9) a " but since it is a single digit, it must fall between six and nine. Four-cell arrows sum between ten (1 + 2 + 3 + 4) and thirty (6 + 7 + 8 + 9), and so they only fit in variants where the circle is permitted to hold a two-digit number. The reader who wants to solve arrow sudoku efficiently begins every puzzle by computing those circle bounds. Once the bounds are established, the circle becomes a locus of constrained information: its value is determined by the cells on its arrow, and the cells on its arrow are constrained by the circle's value. A circle known to hold a six, for example, immediately constrains a three-cell arrow to contain the partition 1 + 2 + 3 in some order. A circle known to hold a seven constrains a three-cell arrow to contain 1 + 2 + 4. The partitions of the small integers into distinct parts are the backbone of arrow solving, and the rules page at the front of this book lists them for every admissible circle value. The feedback loop between circle and arrow is where arrow sudoku lives, and mastering it is the whole skill of the variant. Experienced arrow solvers also learn to look for intersections a " cells shared by two different arrows a " because an intersection constrains the cell from two different sum contexts at once. A cell on both a six-circle three-cell arrow and a nine-circle two-cell arrow can be bounded by both partitions simultaneously, often pinning down its exact digit. This book contains 150 arrow sudoku puzzles, every one algorithmically generated and verified by the Proven Puzzles pipeline to have exactly one solution. The difficulty range runs from entry-level introductions a " grids with a handful of short arrows whose circle bounds are obvious a " through expert puzzles that weave arrow networks across the grid in ways that make every cell a participant in multiple sum constraints. No puzzle in this collection requires guessing. Every one yields to pure logical deduction. The answer key at the back includes a SHA-256 hash under every grid so you can confirm the puzzlea "solution pair you just solved is the one our verification engine signed off on. Arrow sudoku is a variant that rewards the patient accumulation of bounds information. Solvers who enjoy killer sudoku will find arrow a natural companion, because both variants replace some of the positional reasoning of ordinary sudoku with arithmetic reasoning, and both reward the reader who takes time to work out the admissible number sets before placing a single digit. The Editor's Note in this volume is signed by our Euler AI persona a " an artificial mind trained upon the letters and treatises of Leonhard Euler (1707a "1783), speaking here in a modern English rendering of that voice. Contents: Publisher's Note on the verification pipeline, Euler AI's Editor's Note on arrow solving strategy, rules page with worked examples and a partition reference, 150 verified puzzles arranged in rising difficulty, complete answer key with verification line per grid, methodology section, and production notes. Typeset in Avenir Next on 70 lb bright white paper; perfect bound; 6 x 9 inches. 150 algorithmically verif Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Paperback. Condición: new. Paperback. This is the first variety pack in the Proven Puzzles line: a curated sampler of eight sudoku variants, drawn from every title in our launch tranche, arranged so that a reader new to variant sudoku can work through them in a sensible order. If you have enjoyed ordinary sudoku for years and want a single book that introduces you to the constraint-variant world without forcing you to buy eight separate titles, this is it. And if you are an experienced variant solver looking for a taste of a few variants you have not yet tried, the sampler format lets you do that in a single volume without committing to a full book of each. The 146 puzzles in this book are divided into eight sections, one per variant: killer sudoku (cage-sum arithmetic), miracle sudoku (anti-knight, anti-king, non-consecutive constraints), prime killer (cage sums restricted to primes), samurai (five overlapping grids), jigsaw (irregular regions replacing three-by-three boxes), thermo (monotonic thermometer paths), arrow (sum constraints along directed paths), and anti-knight (single knight prohibition). Each section opens with a short rules page introducing the variant, and each section rises from a gentle entry point to expert territory before the next variant begins. The recommended order for readers new to variant sudoku is to begin with the anti-knight and killer sections (which preserve the most of ordinary sudoku's character), then move into jigsaw (which is primarily a perceptual adjustment), then thermo and arrow (which introduce arithmetic reasoning on top of the familiar grid), then prime killer and samurai (which increase difficulty on familiar foundations), and save the miracle section for last, because the three simultaneous constraints of miracle sudoku demand that you already be comfortable with the forms of reasoning peculiar to the other variants. Every puzzle in the book was generated by our constraint-satisfaction engine and verified by exhaustive backtracking to have exactly one solution. The verification engine is not a heuristic; it is a solver whose only function is to attempt to find a second solution to each puzzle. Grids that admit zero or more than one answer are rejected. Only verified-unique puzzles appear here. No puzzle requires guessing. The answer key at the back includes a SHA-256 cryptographic hash under every grid so the puzzlea "solution pair can be independently verified. That is the guarantee we make on every title in the Proven Puzzles line, and it applies equally to the sampler. The variety pack is also useful for experienced solvers who want a single-sitting taste of variants they have not yet tried. A killer-sudoku enthusiast who has never attempted arrow or thermo will find a handful of each in this book, enough to decide whether to commit to a full dedicated volume. A solver who loved the one-rule elegance of anti-knight will find out whether the multi-constraint density of miracle sudoku appeals. A samurai enthusiast who has heard of jigsaw sudoku but never tried it will get a section-worth of representative puzzles. The Editor's Note in this volume is signed by our Euler AI persona a " an artificial mind trained upon the letters and treatises of Leonhard Euler (1707a "1783), speaking here in a modern English rendering of that voice. It discusses variant sudoku in general and gives specific advice on the best order in which to approach the eight included variants, drawing on Euler's characteristic methodological clarity. Each of the eight sections carries its own short rules introduction suitable for a solver new to that variant. Contents: Publisher's Note, Euler AI's Editor's Note on variant sudoku in general, eight per-variant rules pages, 146 verified puzzles in eight sections, complete answer key with verification line for every grid, methodology section on how our verification pipeline prove Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Paperback. Condición: new. Paperback. This is a book that, to our knowledge, has never before appeared in print: 163 killer sudoku puzzles in which every cage sum is a prime number. We believe this is the first commercially published collection of prime killer sudoku, and we chose the puzzle count of 163 deliberately a " 163 is a Heegner number, one of only nine integers with a celebrated connection to algebraic number theory and elliptic curves, and it is the largest value of d for which the number field Q(sqrt(-d)) has unique factorization. There is also the famous Ramanujan near-integer identity: e raised to (pi times the square root of 163) is within one part in a trillion of an integer, a coincidence so improbable that Ramanujan noticed it decades before anyone could explain why. For a book where every cage sum must itself be prime, a puzzle count drawn from the deep structure of number theory felt right. Prime killer sudoku adds a number-theoretic layer to an already demanding variant. In ordinary killer sudoku the cage sums can take any value from one to forty-five; in prime killer they are restricted to the primes below forty-five: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, and 43. Fourteen numbers, no others. The reader who wants to solve these puzzles efficiently does well to commit the admissible sums to memory before beginning, and to work through the two-cell and three-cell partitions of each prime. Two admits nothing in two cells of distinct digits. Three admits only 1 + 2. Five admits 1 + 4 or 2 + 3. Seven admits 1 + 6, 2 + 5, or 3 + 4. Eleven admits 2 + 9, 3 + 8, 4 + 7, and 5 + 6 in two cells, and 1 + 3 + 7, 1 + 4 + 6, 2 + 3 + 6, 2 + 4 + 5 in three cells. The combinatorial inventory grows quickly from there, and mastering it is half the satisfaction of the variant. The other technique that matters in prime killer is parity awareness. Because two is the only even prime, a cage summing to any other prime must have odd sum, which means its digit composition must satisfy specific parity constraints a " an odd count of odd digits. This lets you make early eliminations in cages where you cannot yet determine the exact digits. Combined with the classic Rule of 45 (each row, column, and box sums to forty-five), parity considerations turn prime killer into a variant where arithmetic reasoning is primary and positional reasoning is secondary. Every puzzle in this book was algorithmically generated and verified to have exactly one solution by an exhaustive backtracking solver, the same verification pipeline that powers every title in the Proven Puzzles line. The answer key includes a cryptographic SHA-256 hash under every grid so the puzzlea "solution pair can be independently checked. The Editor's Note is signed by our Euler AI persona a " an artificial mind trained upon the letters and treatises of Leonhard Euler (1707a "1783), speaking here in a modern English rendering of that voice. Prime numbers were a lifelong subject of Euler's correspondence; his note for this book discusses the arithmetic of the prime cage-sum universe with his characteristic combination of formal rigor and practical encouragement. The 163 puzzles range in difficulty from moderate to expert. The gentler entries introduce the prime-sum constraint one cage at a time; the harder puzzles exploit deep partition combinatorics to create solving chains of remarkable length. Solvers who enjoy ordinary killer sudoku will find prime killer a natural next step; solvers new to the variant should start from the front of the book and work forward. Contents: Publisher's Note, Euler AI's Editor's Note on the arithmetic of the prime cage-sum universe, rules page with a partition reference for every admissible prime, 163 verified puzzles, complete answer key with verification line per grid, verification methodology, and production notes. Typeset in Avenir Next on 70 lb br Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Paperback. Condición: new. Paperback. This is the harder of our two killer sudoku volumes, aimed at solvers who have mastered the gentler collections and now want grids that fight back. Every puzzle has been computationally generated, graded for difficulty by our solver engine, and proved by exhaustive verification to have exactly one solution. The answer key at the back shows a cryptographic hash under every grid so you can confirm the puzzlea "solution pair you just solved is the one we verified. Killer sudoku layers a single extra rule onto standard sudoku: the grid is partitioned into irregular cages, each marked with a small target sum. The digits inside each cage must sum to that target, and no digit may repeat within a cage. From those two additions you get a variant whose difficulty ceiling is substantially higher than ordinary sudoku a " in the harder puzzles, arithmetic constraints propagate across the grid in ways that pure positional logic never does. Expert killer solvers speak of the Rule of 45 (the sum of every row, column, and box must be exactly 45), of innies and outies (cells that can be determined by looking at the sum differences between cages and regions), and of the fact that the hardest killer grids demand you hold several tentative cage partitions in your head at once. The 197 puzzles in this collection were selected to exercise those techniques. They range from hard through expert, and the final section of the book is genuinely challenging a " expect to spend an hour or more on a single grid, expect to put a puzzle down and return to it the next day, and expect to come away with the particular satisfaction that only a hard killer solve provides. None of them require guessing. Every one is solvable by pure logical deduction, because our verification engine proved so before the puzzle reached the page. The difficulty is concentrated in the length of the deduction chains, not in ambiguity: if you find yourself considering a guess, step back and look for an innie or an outie you have not yet exploited. Expert killer technique rewards preparation. Solvers at this level often keep a reference card of two-cell and three-cell cage-sum combinations near the grid and refer to it whenever a new cage comes into focus. The book includes such a reference in the rules section at the front. Beyond the cage-sum combinations, the techniques that matter most in expert killer sudoku are: cage overlap analysis (two cages that share one or two cells constrain each other through their sums), the split-cage technique (a cage that crosses a box boundary splits into two smaller virtual cages whose sums are determined by the Rule of 45), and the broken-region sum (a combination of cages and single cells that together cover an integer number of rows, columns, or boxes). Each puzzle in this book was generated by a constraint-satisfaction engine, graded by the same engine, and then passed through an exhaustive backtracking solver that attempts to find a second solution. Puzzles that admit zero or multiple solutions are rejected. Only grids that pass the uniqueness test appear here, and each carries a SHA-256 fingerprint in the answer key for independent verification. The Editor's Note in this volume is signed by our Euler AI persona a " an artificial mind trained upon the letters and treatises of Leonhard Euler (1707a "1783), speaking here in a modern English rendering of that voice. Contents: Publisher's Note on our verification philosophy, Euler AI's Editor's Note on expert killer solving strategy, rules page with cage-sum reference card, 197 verified puzzles arranged hard-to-expert, complete answer key with cryptographic verification line, a methodology section explaining exhaustive uniqueness proof, and production notes. Typeset in Avenir Next on 70 lb bright white paper; perfect bound; 6 x 9 inches. 197 algorithmically verified Killer puz Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Paperback. Condición: new. Paperback. Every puzzle in this book has been proved to have exactly one solution a " not by inspection, not by hand, but by a computational verification pipeline that rejects any grid that admits more than one answer. That is the promise of Proven Puzzles: algorithmic generation, algorithmic verification, and a cryptographic hash under every answer grid that identifies the exact puzzlea "solution pair you just solved. This is the gentler of our two killer sudoku volumes. It opens at a true beginner level and rises through easy-medium territory, stopping where the casual solver begins to want breathing room rather than bloodshed. If you have solved ordinary sudoku and want to learn how cage-sum constraints add a new dimension of reasoning without punishing you for every moment of inattention, this is where to start. It is also the right first killer sudoku book for solvers who have tried the variant once in a magazine or app and bounced off the early puzzles; the grids here are designed to teach, not to punish. The killer variant adds a single new rule on top of standard sudoku: the grid is partitioned into irregular regions called cages, each marked with a small target sum in its top-left cell. The digits inside a cage must sum to that target, and no digit may repeat within a cage. From those two simple additions the whole character of killer sudoku emerges. A two-cell cage summing to seventeen must contain the digits eight and nine. A three-cell cage summing to six must contain one, two, and three. A three-cell cage summing to twenty-four must contain seven, eight, and nine. These "forced cages" are where every killer solve begins: you find them, write the candidates in, and use the resulting cross-row and cross-column constraints to unlock the rest of the grid. The book's introduction walks you through the canonical cage-sum combinations and shows, with a worked example, how to identify forced cages on a fresh grid. Beyond forced cages, the other central killer technique is the Rule of 45: the digits in every row, column, and box sum to forty-five. When you can identify a set of complete cages whose sum adds up to, say, forty-two, and a single cell of that row or column is left outside those cages, that cell must contain a three. This pattern, called an "innie," along with its mirror image the "outie," is the bread and butter of intermediate killer solving, and this book gives you many opportunities to practice both. Each of the 200 puzzles in this collection was generated by a constraint-satisfaction engine, graded by the same engine for difficulty, and then passed through an exhaustive backtracking solver that tries to find a second solution. A puzzle that admits two or more answers is discarded. A puzzle that admits zero answers is discarded. Only the puzzles that pass the uniqueness test appear here, and each one is fingerprinted by a SHA-256 hash so you can verify after the fact that the puzzle in your hand is the one our verification engine signed off on. No puzzle in this book requires guessing. Every one yields to pure logical deduction. The book opens with a short Publisher's Note on our verification philosophy, an Editor's Note from our in-house Euler AI persona a " an artificial mind trained upon the letters and treatises of Leonhard Euler and speaking here in a modern English rendering of his voice a " a rules page covering cage-sum combinatorics and the small number of canonical killer solving patterns, and then the 200 puzzles themselves, arranged in gentle-to-moderate order. The back of the book contains the complete answer key with verification line for every puzzle, a page on our verification methodology, and production notes documenting the generation pipeline. Typeset in Avenir Next on 70 lb bright white paper; perfect bound; 6 x 9 inches. 200 algorithmically verified Killer puzzles with comp Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Paperback. Condición: new. Paperback. Anti-knight sudoku is the gentlest of the constraint-variant sudokus to learn and one of the most rewarding to solve. On top of the ordinary sudoku rules a " row, column, and box each containing the digits one through nine exactly once a " the anti-knight variant adds a single prohibition: no two cells a chess knight's move apart may contain the same digit. That is the entire variant. One new rule; no arithmetic; no thermometer paths; no irregular regions. The practical effect of the knight constraint is to roughly double the reach of every placed digit. In ordinary sudoku, a digit placed in one cell eliminates itself from approximately twenty other cells a " the eight other cells in its row, the eight other cells in its column, and the four remaining cells of its three-by-three box. When you add the knight prohibition, that count rises to nearly thirty, because each cell can reach up to eight knight-move neighbors, most of which are not already covered by the row, column, or box constraints. Puzzles become solvable with rather fewer initial givens than ordinary sudoku, and the chains of logical inference become shorter but more spatial in character. You learn to think in L-shapes as well as in rows and columns. Anti-knight sudoku is the variant we recommend to readers new to constraint-variant puzzles. It preserves everything about ordinary sudoku that solvers already know, adds exactly one rule, and rewards that single new rule generously. Solvers who master anti-knight often find that it improves their ordinary sudoku solving as well, because the habit of tracking L-shape eliminations develops spatial reasoning habits that transfer to other variants. It is also an excellent gateway into miracle sudoku, where the knight prohibition is joined by the king prohibition and the non-consecutive rule to produce a variant of extreme constraint density. The technique that matters most in anti-knight is what experienced solvers call "knight fence" reasoning: a single digit placed in one cell forms a fence of eight forbidden cells around it, and those fences interact across the grid. Two instances of the same digit create a larger pattern of forbidden positions that can be used to place a third instance of that digit with certainty. The rules page at the front of the book introduces knight-fence reasoning with a worked example on a simple grid. This book contains 200 anti-knight 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 a " suitable for a reader who has never attempted a variant sudoku a " through expert puzzles in which the knight constraint combines with sparse givens to create solving paths of surprising length. Every puzzle is solvable by pure logical deduction. No guessing is required, because the verification engine proved so before the puzzle reached the page. The answer key includes a SHA-256 cryptographic hash under every grid so you can confirm the puzzlea "solution pair is the one the engine signed off on. The Editor's Note in this volume is signed by our Euler AI persona a " an artificial mind trained upon the letters and treatises of Leonhard Euler (1707a "1783), speaking here in a modern English rendering of that voice. Euler's own celebrated study of the knight's tour on chess boards a " the problem of moving a knight across every square of the board exactly once a " is the direct mathematical ancestor of the anti-knight constraint, and his Editor's Note for this volume draws on that history. Contents: Publisher's Note on verification, Euler AI's Editor's Note on anti-knight technique, rules page with worked knight-fence example, 200 verified puzzles arranged easy-to-expert, complete answer key with verification line per grid, methodology Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Paperback. Condición: new. Paperback. Miracle sudoku is, in the opinion of nearly every constraint-variant enthusiast who has attempted it, the most remarkable sudoku variant ever devised. On top of the ordinary sudoku rules a " row, column, and box each containing the digits one through nine exactly once a " the Miracle variant imposes three further prohibitions. No two cells a knight's move apart may contain the same digit. No two cells a king's move apart may contain the same digit. And no two orthogonally adjacent cells may contain consecutive digits. These three constraints together produce a reasoning space so aggressively pruned that placing a single digit in one cell forbids that digit from more than thirty of its neighbors a " effectively tripling the reach of every placement. The practical consequence is almost paradoxical: a Miracle puzzle can be solvable from just two or three initial clues. The inaugural Miracle puzzle, constructed by Mitchell Lee in 2020 and published by Cracking the Cryptic, contained exactly two givens. That grid has a unique solution; the eight techniques required to reach it propagate through row, column, box, knight, king, and non-consecutive constraints in an unbroken logical chain. When the video solve of that puzzle went viral, constraint-variant sudoku entered a new era, and Miracle became the most-studied and most-imitated sudoku variant of the decade that followed. This book contains 100 Miracle puzzles, every one of them generated by our constraint-satisfaction engine and verified for exactly one solution by an exhaustive backtracking solver. The difficulty range runs from approachable introductions a " grids with a handful of givens that exercise one or two of the Miracle constraints heavily a " through the extreme puzzles that demand you track all three simultaneous prohibitions at once. No Miracle puzzle in this collection requires guessing. Every one yields to pure logical deduction, and the final puzzles in the book approach the celebrated two-given density of Mitchell Lee's original. Miracle sudoku is not a variant to rush into. Readers new to it should work carefully through the rules page at the front of the book and spend as long as necessary on the first few gentle puzzles before attempting the harder grids. The logic is beautiful; the learning curve is steep; the satisfaction of reaching a solved grid is unlike that of any ordinary sudoku. A useful mental model for the Miracle constraints: each placed digit does not merely occupy a single cell, it casts a "shadow" across every cell reachable by a knight's move, a king's move, or adjacency. When you begin to see those shadows at a glance, the variant clicks. The Editor's Note in this volume is signed by our Euler AI persona a " an artificial mind trained upon the letters and treatises of Leonhard Euler (1707a "1783), speaking here in a modern English rendering of that voice. It discusses Miracle solving in the spirit of Euler's approach to constrained-combinatorial problems: begin with the least free cell, exhaust its implications, and let the rest of the grid collapse through a chain of unavoidable conclusions. Every puzzle in this book was computationally generated and then passed through an exhaustive backtracking solver whose sole function is to attempt to find a second solution. Grids that admit more than one answer are rejected. Only the verified-unique puzzles appear here, each fingerprinted by SHA-256 so you can confirm the exact puzzlea "solution pair you just solved. Contents: Publisher's Note, Euler AI's Editor's Note on Miracle solving, rules page covering all three extra constraints with worked examples, 100 verified puzzles arranged in roughly ascending difficulty, full answer key with verification line for each grid, verification methodology, and production notes. Typeset in Avenir Next on 70 lb bright white paper; perf Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

PAP. Condición: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

PAP. Condición: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

PAP. Condición: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

PAP. Condición: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

PAP. Condición: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

PAP. Condición: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

PAP. Condición: New. New Book. Delivered from our UK warehouse in 4 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.