Euler AI
Thermo sudoku takes the ordinary sudoku grid and overlays it with a set of thermometer paths. Each thermometer has a bulb (the rounded end) and a tip (the pointed end), and the rule is brief and elegant: digits along the thermometer must increase strictly from bulb to tip. A two-cell thermometer admits only pairs where the second digit exceeds the first. A seven-cell thermometer must begin with a 1, 2, or 3 at its bulb and end with a 7, 8, or 9 at its tip; the length of the path imposes immediate and unbreakable bounds on every cell along it.The thermometer rule is the simplest one-line constraint in the variant-sudoku catalog, and the consequences are among the richest. Solvers new to the variant quickly learn to count thermometer length before placing any digit: a length-seven thermo gives you more information than any givens in the grid. A length-nine thermometer is its own complete solution â€' it must contain the digits one through nine in order. Experienced solvers learn to look for thermometer intersections, where two monotonic paths share a cell, because intersections constrain the grid from two directions at once. A cell shared by a length-five thermo starting at one bulb and a length-four thermo starting at another can be independently bounded from both sides, and the intersection of those bounds is sometimes enough to determine the cell’s digit entirely.This book contains 150 thermo sudoku puzzles, every one generated by the Proven Puzzles pipeline and verified to have exactly one solution by exhaustive backtracking. The difficulty range runs from entry-level introductions â€' grids with a handful of short thermometers and a few traditional givens â€' through expert puzzles in which the thermometer network is dense enough to replace traditional givens almost entirely. At the expert end, some puzzles have no digit givens at all, only a network of thermometers; the monotonic constraints propagate across the whole grid and the solve proceeds entirely from path analysis.The other key technique in thermo sudoku is the 'thermometer parity' observation: a thermometer of length k occupying cells in a row, column, or box constrains the sum of those cells. In particular, because the digits along a length-k path must be strictly increasing, the minimum possible sum of the path is 1 + 2 + 3 + ... + k, and the maximum is (10−k) + (11−k) + ... + 9. When a thermometer is partially contained in a row or column, this gives you an immediate inequality on the sum of the other cells of that row or column, which can sometimes be combined with the standard Rule of 45 to pin down exact values.No puzzle in this collection requires guessing. Every one yields to pure logical deduction. The verification pipeline rejects any grid that admits zero or multiple solutions, and the puzzles that appear in this book are fingerprinted by SHA-256 in the answer key so you can confirm the exact puzzleâ€'solution pair. 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 â€' and it discusses thermo technique with an emphasis on the thermometer-length-first heuristic that every experienced solver learns within their first ten puzzles.Contents: Publisher’s Note on the verification pipeline, Euler AI’s Editor’s Note on thermo technique, rules page with worked examples, 150 verified puzzles arranged from gentle to expert, 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.
