Keep your mind young with Sudoku. How to solve sudoku -- easy rules.

Index:

Benefits of Sudoku

  1. Fun.
  2. Some teachers recommend Sudoku as an exercise in logical reasoning.
  3. Exercises the brain cells.
  4. It is claimed (but not yet proved) that Sudoko can defer the onset of Alzheimer's.

Basic Rules to solve Sudoku

First, the lay of the land

In your newspaper or book, you will see a Sudoku puzzle, a grid, usually of 9 rows and 9 columns, giving 81 cells in a 9x9 grid:
                                               
 
 
 
 
 
 
 
 

Within a grid, cells are grouped into boxes. In a 9x9 grid, they are grouped into 9 boxes, each of 3 rows and 3 columns. Thus there are 9 cells in a box. And there are 9 boxes in a grid.

                               
 
 
 
 
               
                               
 
 

It can be useful to focus in turn on each horizontal band, which is a set of three boxes adjacent horizontally:

                               
 
 

After that, it can be useful to focus in turn on each vertical stack, which is a set of three boxes adjacent vertically:

               
 
 
               
 
 

Second, look at the puzzle you are solving

Between a quarter and a third of the cells contain a given initial value. The rest are empty and your challenge is to discover every unknown value.

This is a game of logic. You can be especially brave by writing your solution in PEN. Sudoku is not like a crossword puzzle, where more than one answer might be correct, at least temporarily. A delight of sudoku is that every proper puzzle has a unique solution, and only one value is correct for each cell.

Your goal is to fill in the grid so every cell in a row has a different symbol. Also every cell in a column must have a different symbol. And every cell in a box must have a different symbol. For a 9x9 grid, the symbols are the numbers from 1 to 9.

Scanning

Scanning is the best way to begin. You can win a lot of success by scanning, which you do by using these two techniques: cross-hatching and counting.

  1. Cross-hatching.

    This is especially useful in the opening game.

    Initially, this technique is more manageable if applied to each band in turn and then each stack.

    Start with the top band, which is the top set of 3 boxes. Do you see any digit that occurs in two of the 3x3 boxes? If you do, notice that the digit is shown both in:

    1. two different rows, leaving only one row without that digit and needing it; and
    2. two different boxes, leaving only one box without that digit and needing it.

    That will give you one to three candidate cells. If there is only one candidate cell, then you have discovered a singleton: enter the digit into the empty cell. For example

      4                            
     
        4

    The only possible value that can go at the Candidate '4' goes here. (6th column of 2nd row) is a 4.

    If there is more than one candidate cell, check if the digit of interest appears in one or two of the vertical columns: this is the 'Cross-hatching' part. If that leaves you with only one candidate cell, you have discovered a singleton: enter the digit into the empty cell.

    Continue for any other digits that appear twice in the top band, to discover all the top-band singletons.

    Do the same thing for the middle band.

    And finally for the bottom band.

    Now you are ready to do the same thing by scanning the stacks. Begin with the left-most stack, which is the set of 3 boxes on the left of the grid. Do you see any digit that occurs in two of those 3x3 boxes? If you do, notice that the digit is shown in

    1. two different columns, leaving only one column without that digit and needing it.
    2. two different boxes, leaving only one box without that digit and needing it.

    Continue in a similar way to the way you scanned for the top band.

    Do the same thing for the middle stack.

    And finally for the right-most stack.

    Of course, by the time you have done all this, you have entered values in a lot of cells. So repeat the cross-hatchin until you can find nothing more.

  2. End-game Counting. Sometimes, especially toward the end of the game, you notice there are only a few blank cells in any one box, row, or column.

    For each of the most-filled rows, columns, and boxes, in turn identify which digits (of 1-9) are missing.

    See more at middle-game counting.

Quick payoff hint

* TIP * After discovery of another digit, perform one of the scanning techniques, focusing on that digit.


Intermediate Rules to solve Sudoku

  1. Middle-game counting.

    In the basic rules, we saw that the straight-forward application of counting can be useful in the end-game of the whole grid or of a particular column, row, or box.

    It can also be useful in letting you identify (say) a pair of values that must be in two cells. Although you are not able to fill in those values (either could go in either cell), this information can reduce the number of possible values for cells of an intersecting box, row, or column.

  2. Stack and band elimination.

    A subset of the above middle-game counting, whereby one determines certain values that cannot go in a cell, though their exact location elsewhere (in an associated box, row, or column) is still being worked out. See Teach Yourself Sudoku.

  3. Hidden Pairs.

    See Teach Yourself Sudoku.

  4. X-Wing.

    This highly advanced technique is used when cells at the corners of any-size rectangle have pairs of candidates, each with a common candidate number. While you don't know where the candidate number goes, you do know that it must be in diagonally opposite corners.

    This clever technique lets you eliminate any other instances of this candidate from the rest of the non-corner sides of the rectangle.

    See Teach Yourself Sudoku for an example that happens to use the numeral 6.


Glossary.

  1. Area.
    9 cells that form a box, row, or column.

  2. Band.
    Three 3x3 boxes, adjacent horizontally. There are three in a 9x9 Sudoku grid.

    Block.
    Alternate name for box: one of the 3x3 sets of cells in a Sudoku 9x9 grid.

    Box.
    In a Sudoku 9x9 grid (the most common Sudoku grid) there are 9 boxes. Each box has 3 rows and 3 columns, for a total of 9 cells.

  3. Candidate.
    A potential value for a cell.

    Cell.
    In a Sudoku grid, a field that will hold a single symbol. The most common Sudoku grid is the 9x9, with 9 rows and 9 columns, for a total of 81 cells.

    Column.
    In a Sudoku grid, there are 9 columns, each of 9 cells. In the solution of a 9x9 Sudoku, each of those cells holds a unique digit from 1 to 9.

    Counting.
    A technique of Scanning. See also Cross-hatching.

    1. For each of the most-filled rows, columns, and regions, in turn identify which of 1-9 are the missing digits.

    Cross-hatching.
    A technique of Scanning. See also Counting.

    1. Start with digit 1.
    2. Scan rows to identify if a single line in a region is missing this digit.
    3. Do the same for the columns.
    4. If there is a single intersection in a region, you have discovered its value.
    5. Repeat for digits 2-9.
    6. After you develop experience, the discovery may go quicker if you start with the most common digit, and then the second most common, etc. Be sure to check each digit in turn.

  4. Given.
    An initial value displayed in a cell. The rest of the cells, which are blank at the start, are unknowns.

    General memory processes.
    See also general mental processes in cognitive psychology.

    Grid.
    In a Sudoku grid, there are 9 rows, and 9 columns, which results in 81 cells. There are 9 boxes, each of 3 rows and 3 columns, which gives 9 cells in each.

  5. Likely cell.
    An empty cell in a group that is relatively full. The fewer the candidate numbers, the more likely you can find a number for this cell. An effective way to capitalize on the multiple presences of such a number is the counting technique. See especially Advanced Sudoku and Kakuro for rules for developing sudoku expertise.

    Likely number.
    A number that has more entries in the grid than most of the others. An effective way to capitalize on the multiple presences of such a number is the cross-hatching technique. See especially Advanced Sudoku and Kakuro for rules for developing sudoku expertise.

    Line.
    A row or a column.

  6. Mental activity.
    Brain activity. Needed for Sudoku.

    Memory.
    The capacity to recall something learned or to recognize something previously experienced. See also memory in cognitive psychology.

    Mental processes.
    The activities of your brain to handle information, when you think, perceive objects, store information, etc. Active in solving Sudoku. See also mental processes in cognitive psychology.

  7. Proper Puzzle.
    A Sudoku puzzle that has a unique solution.

    Puzzle.
    A Sudoku puzzle is a partially completed grid.

  8. Quadrant.
    Alternate name for box: one of the 3x3 sets of cells in a Sudoku 9x9 grid.

  9. Region.
    A subgrid with the Sudoku grid. In a 9x9 Sudoku grid, a region is 3 cells tall and 3 cells wide, giving a total of 9 cells.

    Row.
    In a Sudoku grid, there are 9 rows, each of 9 cells. In the solution of a 9x9 Sudoku, each of those cells holds a unique digit from 1 to 9.

  10. Scanning.
    Scan to find or eliminate candiate values. Do it at the start of your solution and once between each analysis. Two techniques of scanning:
    1. Cross-hatching.
    2. Counting.

    * TIP * TIP: after discovery of another numeral, perform either scanning technique based on that numeral, for possible quick payoff.

    Singleton.
    A cell for which there is only one remaining candidate.

    Stack.
    Three 3x3 boxes, adjacent vertically. There are three in a 9x9 Sudoku grid.

    Sudoku.
    A subgrid with the Sudoku grid.

  11. Tower.
    Three vertical cells in a box. Each box has three towers.

  12. Unknown.
    A cell with no initial value displayed. The cells with values shown at the start are givens.


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