Unlike the puzzles themselves the rules to sudoku are fairly simple. Each puzzle consists of 81 sqares. Those sqares are divided up into 9 rows and 9 columns, and 9 blocks. When the puzzle is solved, every row, column, and block will have each of the numbers 1 through 9 in it. All you have to do to play is to fill in the empty blocks by figuring out which numbers belong where. There is only one correct solution to any sudoku puzzle.
For most every sudoku puzzle you will need to use more than one method.
For every square there are nine possible numbers that could fit there. The single candidate method has you list all 9 numbers for any one box, then scratch out any numbers that cannot fit in that box. Scratch out all the known numbers that are in the same row, block and column. If you end up with only one number left in the possible list, that box is solved.
In the example picture, by eliminating all the possiblites within the same row, column, and block, there is only one number left. Therefore that box is solved and it must be a four.
The principal behind this method lies in the transition from horizontal to vertical to perform elimination. If the only place a given number can be within a 3x3 block is on only one row or one column, that number has to be in that row or column inside that block. That means that number can be removed as a candidate from the other boxes outside that block along the same row or column.
In the example, there has to be a three in the blue squares because there is no possible place elsewhere within that block that a three could be. Since a three has to be on the bottom line in that block, none of the other squares along that line can be a three.
The double pairs method is another elimination tactic. If a number can only be in two columns on a given row, and in the same two columns in anther row, that number must be in one place on one row, and in the other on the other row. It doesn't matter which is right, what matters is that no other boxes in those columns can have that number in them.
Looking at the example, the blue squares mark the double pair of sevens. If in the top line the left blue square ends up bieng seven, the one on the right in the bottom line will also be a seven. If on the top line the right blue square ends up bieng seven, the one on the bottom left will also be seven. We can't figure out which will end up bieng correct using this method. We can tell that seven will be in either the top or the bottom blue square in both columns. Therefore it isn't possible for a seven to be anywhere else in either column. The red marks represent scratched out seven's that could have been eliminated becuase of this rule.
I've seen this one explaind in a rather complicated manner involving figuring what lines a number can be on to figure out what lines it cannot be on. For me this method is one of the easiest to spot. Put simply, If on one row a number can only be within a given block, that number cannot be elsewhere within that block.
In the example above, the numbers one through 6 are eliminated because they are already used in the row. Therefore seven eight and nine have to be the numbers left. Since they have to be in the bottom line in the block, they can be eliminated from all the other boxes within the block.
If same two numbers are the only two possibilities in two different squares within a line or block, those two numbers have to go into those two boxes one way or the other. Therfore, you can eliminate those two numbers from the other boxes within that line or block.
In the example above, the blue squares represent a naked pair. Since the one and the five have to be in one or the other of the blue squares, we can eliminate the one and the five from all the other boxes along that row. This reduces the possibilites in the first box and solves the seventh box.
Note that naked pairs can come in naked triples, naked quads, ect. However for a triple it requires a set in three squares a quad requires four, and so on.
The hidden pairs method is the same as the naked pairs method. It just happens that the pair is obfuscated by an extra number or two to confuse you. The pair is still there, its just harder to spot.
In the example above the blue squares represent a hidden naked pair. If the blue box on the right were a two, the one on the left would have to be a four. If the one on the right were a four, the one on the left would end up having to be a two. Therefore it isn't possible for the box on the left to be a one and we can strike the one from the possible candidate list. Also note that the three other unsolved boxes make up a naked triple. There is often more than one way to solve a box.
I know I haven't exactly done a fantastic job of explaining some of the solving methods. In truth I still have a difficult time visualizing several of the more complicated rules. Xwing and swordfish come to mind. You can use this search box to find other explanations. Sometimes understanding the concept is just easier if its explained differently or by someone else. Note that I have conviniently skipped explaining some of the most difficult methods. Its rather difficult to teach them when I have a hard time with them.
Tip Try searching for sudoku techniques, or sudoku tips. both pull up a good list of helpful results.
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