Sudoku is a graphical logic puzzle in which the solver must place the digits from 1 through 9 into empty boxes according to certain rules. In a standard sudoku puzzle, a 9 by 9 grid is divided into nine boxes, each with nine squares. Each row, column, and box must contain every digit from 1 to 9 exactly once. Applying solving techniques in an orderly way enables beginners to do sudoku puzzles with minimal frustration.
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Check each row, column, and box to see if exactly eight of the digits are already filled in. Wherever this is the case, place the missing number in the empty box.
Use the scanning technique on the top row of boxes for each digit, working from 1 to 9. If the digit is in all three boxes, move to the next digit. If the digit is in two boxes, look at the row in the remaining box. If there is only one open box in that row, place the digit there and move to the next digit. If there are several open boxes in the row, scan the entire nine-square column under each open box. If all but one empty box has that digit in its column, place the digit in the remaining box and move on to the next digit.
Move to the middle row of boxes and apply the same scanning technique for each digit from 1 to 9. Repeat for the bottom row of boxes in the same manner.
Move to the left column of three boxes and apply the scanning technique to each column, using the same methods used for the rows, but with directions switched. Repeat for the middle and right columns of boxes.
Go back to Step 1 and repeat this procedure. Each time you fill in numbers in rows, new information is available to scan columns, and vice versa. This procedure may be enough to solve some puzzles without continuing to the next step. Repeat this technique until you can no longer place any more digits.
Use the single-square technique on empty squares in rows, columns, or boxes that are almost complete (i.e., that have few empty squares remaining). Select an empty square and check for the digits 1 through 9 in its row, column, and box. If eight digits can be found, place the missing digit in the square. Repeat this technique for every empty square in each nearly-complete row, column, and box.
Repeat these steps as needed until the puzzle is solved.
Tips and warnings
- Double-check your work as you go. If you make a mistake early on, you will get stuck later and will have to erase all your work and start over.
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