![]() ![]() Thus the middle box needs put it in the lowest row, which has OOCR. 8 (6, 1)Įach of the bottom 3 rows must have an "8", each in a different box. Column 1 has two empty cells, but the lower one is disqualified by the "8" in its row. ![]() The same top left box needs an " 8." It cannot be in column 3 (it is fall filled in that box), nor in column 2 (it already has an 8). Note: this could already have been deduced as step The top box in the first stack (left top) needs a " 9," and we have OOCR. Often after you have filled a cell (as in step, it is a good idea to look around (in many cases nearby-but sometimes not) and see if that step has helped fill another cell.Īpplying SR-1 (see ) to the 3 appearances of "9" in the 3 columns furthest to the left. Note that again, only steps and have made this possible. It cannot be in the 3rd column (which has a "5" already), nor in the bottom row (same reason). There must exist a " 5" in the same bottom left box. Try to find the "natural order" of steps! Thus naturally follows as we go from the easy part to the more difficult. Note that only step allowed this deduction. It cannot be in its bottom row (which already has a 9), nor in the left column (same reason). There must be a " 9" somewhere in bottom left box. There is only one choice remaining ( OOCR for short). Two empty cells exist there, but the one in the last column is disqualified, because there already is a "4" in it. Following the above example, we expect a "4" in one of the bottom cells of the middle box on the bottom. In using rule SR-1 for a row, look for columns which disqualify some cells.Įach of the 3 rows of the bottom boxes needs a "4", each in a different box. In using rule SR-1 for a column, look for rows which disqualify some cells. Two empty cells exist in the column, but the top one is disqualified, because the same row already contains a "4" and the same number cannot appear in it twice. Similarly, If 3 boxes contain 3 parallel rows, the same number must appear in each row in a different box.Īrguing as in, there must be a "4" in the middle column of the bottom box in the middle stack. Solution rule SR-1: If 3 boxes contain 3 parallel columns, the same number must appear in each column in a different box. No number may be repeated, none can be left out.įilling the Missing NumbersNumbers entered as part of the solution will be introduced in the order in which they are derived, numbered in parenthesesĮach of the 3 boxes in the first stack on the left must contain a " 6", each in a different column.The top and middle boxes have it in columns 1 and 2, therefore the bottom box) must have it in column 3. (distinguishing bottom, top or middle tiers)Įvery column, row and box must contain all the nine numbers 1,2,3. Three boxes in a horizontal row will be called a tier (distinguishing left, right or middle stacks) Three boxes in a vertical columns will be called a stack To define the positions of boxes, it is easiest to classify them by stacks and tiers: In each row, cells are numbered from the left.Ī notation like 6 (3,2) will mean the number "6" in cell 2 of column 3Įxtra division lines (or darker ones) divide the array into 9 boxes, each with 3 rows of 3 cells each. Or else, it can be divided into 9 rows (counted from the bottom), each containing 9 cells. In each column, cells are numbered from the bottom. The puzzle consists of a square array of 81 cells, which can be divided into 9 columns, (counted from the left), each containing 9 cells. The challenge of the puzzle is-given just some of the numbers of a specific array, fill in the missing ones, using only logical deduction based on the above requirements. In addition, however, each Sudoku array can be divided into 9 smaller 3-by-3 squares, each of which which also must contain all the numbers (1,2,3.9). 9) in a different order, and the same holds for the columns. Sudoku is a puzzle from Japan, based on what mathematicians call " Latin Squares"-square arrays of numbers in which every number appears exactly once in any row and in any column (different letters, colors or symbols may be used in place of the numbers).Ī Sudoku puzzle contains 9 rows of 9 numbers, each containing (1, 2, 3. Some intermediate steps will be shown, but not all. ![]() The array used is pictured above it is suggested you bring it up on the screen (in larger format) by clicking here, print it and then use a pencil to fill in the empty squares, following the steps outlined below. Follow the steps and you will get a good idea of how to do it. ![]() Solving a Sudoku Puzzle The Goal of the Puzzle, and the Notation Used Here This is a step by step solution of a random Sudoku puzzle, intended to demonstrate the method of solution. Sudoku: step-by-step solution of the puzzle below ![]()
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