Particularly challenging puzzles may require multiple contingencies to be recognized, perhaps in multiple directions or even intersecting - relegating most solvers to marking up (as described below). When those cells all lie within the same row (or column) and region, they can be used for elimination purposes during cross-hatching and counting (Contingency example at Puzzle Japan). It also can be the case (typically in tougher puzzles) that the value of an individual cell can be determined by counting in reverse - that is, scanning its region, row, and column for values it cannot be to see which is left.Īdvanced solvers look for "contingencies" while scanning - that is, narrowing a number's location within a row, column, or region to two or three cells. Counting based upon the last number discovered may speed up the search. It is important to perform this process systematically, checking all of the digits 1–9.Ĭounting 1–9 in regions, rows, and columns to identify missing numbers. For fastest results, the numbers are scanned in order of their frequency. This process is then repeated with the columns (or rows). Two basic techniques comprise scanning:Ĭross-hatching: the scanning of rows (or columns) to identify which line in a particular region may contain a certain number by a process of elimination. Scans may have to be performed several times in between analysis periods. Scanning is performed at the outset and periodically throughout the solution. The strategy for solving a puzzle may be regarded as comprising a combination of three processes: scanning, marking up, and analysing. ![]() Each number in the solution therefore occurs only once in each of three "directions", hence the "single numbers" implied by the puzzle's name. The goal is to fill in the empty cells, one number in each, so that each column, row, and region contains the numbers 1–9 exactly once. Some cells already contain numbers, known as "givens". ![]() The puzzle is most frequently a 9x9 grid made up of 3x3 subgrids (called "regions"). The puzzles are often available free from published sources and also may be custom-generated using software. The level of difficulty of the puzzles can be selected to suit the audience. Sudoku is recommended by some teachers as an exercise in logical reasoning. The attraction of the puzzle is that the completion rules are simple, yet the line of reasoning required to reach the completion may be difficult. Numerals are used throughout this article. Dell Magazines, the puzzle's originator, has been using numerals for Number Place in its magazines since they first published it over 25 years ago. Any set of distinct symbols will do letters, shapes, or colours may be used without altering the rules (Penny Press' Scramblets and Knight Features Syndicate's Sudoku Word both use letters). ![]() See History section, below.) The numerals in Sudoku puzzles are used for convenience arithmetic relationships between numerals are absolutely irrelevant. Ltd in Japan, and other Japanese publishers generally refer to it as "number place". (This name is a registered trademark of puzzle publisher Nikoli Co. The word Sudoku means "numbers singly" in Japanese. Although first published in 1979, Sudoku initially became popular in Japan in 1986 and attained international popularity in 2005. Its grid layout is reminiscent of other newspaper puzzles like crosswords and chess Each row, column and region must contain only one instance of each numeral.Ĭompleting the puzzle requires patience and logical ability. Starting with various numerals given in some cells (the "givens"). ![]() The aim of the canonical puzzle is to enter a numeral from 1 through 9 in each cell of a 9x9 grid made up of 3x3 subgrids (called "regions"), A Sudoku puzzle, sometimes spelled Su Doku, is a logic-based placement puzzle, also known as Number Place in the United States.
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