SUDOKU SOLVING TIPS GETTING STARTED

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1 TTN STRT SUOKU SOLVN TPS Terms you will need to know lock: One of the nine x sections that make up the Sudoku grid. andidate(s): The possible numbers that could be in a cell. ell: single square in a Sudoku grid. To solve a regular Sudoku puzzle, place a number into each cell of the diagram so that each row across, each column down, and each block within the larger diagram (there are of these) will contain every number from through. n other words, no number may appear more than once in any row, column, or block. Working with the seeds already given as a guide, complete each puzzle with the missing numbers that will lead to the correct solution. or example, look at the ninth column of the example puzzle to the right. There are clues in the puzzle that will tell you where, in this column, the number belongs. The first clue lies in the eighth column of the diagram. There is a in the fifth cell. Since numbers can't be repeated in any x block, we can't put a in the fourth, fifth, or sixth cells of the ninth column. We can also eliminate the bottom three cells of the ninth column because there's a in that x block as well. Therefore, the must go in the second or third cell of the ninth column. The final clue lies in the second row of the diagram, which already has a in it. Since numbers can't be repeated within a row, there's only one cell left for the the third cell of the ninth column. The basic elimination process used in the example above results in a irect Solve. The best way to work through a Sudoku puzzle is to tackle the irect Solves first, since they are the easiest. n fact, all easy-level puzzles can be completed using only irect Solves. With more difficult Sudoku puzzles, you will reach a point at which irect Solves no longer exist. t this stage, you need to review the possible candidates for each cell, and then start looking at the relationships among cells to see what candidates you can eliminate. This will eventually reveal the next solvable cell. inding the candidates to eliminate is where advanced solving techniques called eductions come in. There are different deductive techniques that SudokuSolver will point out for you when they are available. elow is a description of each, in order of their complexity. Please note that applying deductions will often result in ndirect Solves. ndirect Solves are similar to irect Solves, except that some of the candidates will have been eliminated via deductions, rather than directly from the solved cells. opyright 00 Penny Publications, LL

2 LOK NT n a locked candidate, a value must appear at the intersection of a particular block and row or column, and can therefore be removed as a candidate from the rest of that block and row or column. n the example at right, we've filled in the candidates for each cell, and the in Row can only be in lock (in other words, none of the cells in Row in either lock or lock have as a candidate). Therefore, can be eliminated as a candidate from all other cells in lock that is, the can be eliminated from. NK PR n a naked pair, two cells in a row, column, or block each contain the same two candidates, and only those candidates. f a naked pair appears in a row, column, or block, those two candidates can be eliminated from every other cell in that row, column, or block. n the example at right, we've filled in the candidates for each cell, and the only possible candidates for cells and are and, forming a naked pair. Since and must be in cells and, in some order, none of the other cells in row can be either a or an (or we could not give values to both and ). Therefore, and can be eliminated from all other cells in row that is, the can be eliminated from, and can be eliminated from, and can be eliminated from. opyright 00 Penny Publications, LL

3 NK TRPLT The naked triplet is similar to the naked pair, but it involves three cells instead of two. n the example at right, cell is or ; cell is,, or ; and cell is or, so in that block,,, and must be in cells,, and, in some order. Therefore,,, and can be eliminated from all other cells in that block. With a naked triplet, some (or all) of the three cells in question may have only out of the candidates, as in our example. N PR n a hidden pair, two numbers are candidates for two different cells in a row, column, or block, and in no other cells in that row, column, or block, even if the two cells in question have other possible candidates. The other possible candidates can then be eliminated from those cells, since those two numbers have to be in those cells (or they wouldn't appear in the row, column, or block). n the example at right, the only cells in row that contain the candidates and are and, so and must be in and in some order, so all other candidates in those two cells can be eliminated. opyright 00 Penny Publications, LL

4 N TRPLT The hidden triplet is similar to the hidden pair, but it involves three cells instead of two. n the example at right, the only cells in column that contain the candidates,, or are,, and, so,, and must be in,, and in some order, so all other candidates in those three cells can be eliminated. X-WN n X-Wing takes into account the interaction between two different rows and columns. f a value in one row can only appear in two different cells, and that same value in another row can only appear in two different cells, and those four cells are in the same two columns, that value must appear in one of those cells in each of the two columns, and therefore can be eliminated from any other cell in the two columns. (The same theory works if you swap rows and columns.) n the example at right, the in column can only be in row or row, and the in column also can only be in row or row. f the in column is in row, the in column must therefore be in row, and if the in column is in row, the in column must therefore be in row. Therefore, the cannot be in any other cells in rows and but,,, or (or we would not be able to place the s in columns and ), so we can eliminate the s from all other cells in those two rows. opyright 00 Penny Publications, LL

5 XY-WN n XY-Wing is a relationship that occurs among three cells that form an angle, where each of the three cells has only two values in it. f the stem of the angle (we'll call it cell ) has the only possible candidates x and y, and the other two cells the branches of the angle (we'll call them cells and ) have the only possible candidates x or z and y or z in some order, no cell that interacts with both of those cells can have the candidate z. f it did, then cells and would have the values x and y, in some order, leaving no possible value for cell. n XY-Wing can appear in two ways with a right angle and without a right angle. XY-WN (With a Right ngle) n this type of XY-Wing, the three cells form a right angle. n the example at right, cell (the stem of the right angle) is or, cell is or, and cell is or. f cell were, then would have to be and would have to be, leaving no possible value for ; therefore, can be eliminated from cell. opyright 00 Penny Publications, LL

6 XY-WN (Without a Right ngle) n this type of XY-Wing, the three cells in question still form an angle, but it is not a right angle. n the example at right, cell (the stem of the angle) is or, cell is or, and cell is or. f cell were, then would have to be and would have to be, leaving no possible value for ; therefore, can be eliminated from cell. SWORS Swordfish is similar to X-Wing, but it takes into account the interaction among three different cells and columns. f a value can only be in two or three of three different cells in each of three rows, and all three of those cells are in the same columns in all three rows, that value must appear in one of those cells in each of the three columns, and therefore can be eliminated from any other cell in the three columns. n the example at right, the in row can only be in column or column, the in row can only be in column or column, and the in row can only be in column or column. f the in row is in, the in row must be in, and the in row must be in ; and if the in row is in, the in row must be in, and the in row must be in. cannot therefore be in any other cells in columns,, or but,,,,, and (or we would not be able to place the s in rows,, and ), so we can eliminate the s from all other cells in those three columns. opyright 00 Penny Publications, LL