Sudoku is a Japanese logic puzzle growing in popularity in Britain and the United States. Meaning "single number" in Japanese, a sudoku consists of a 9-by-9 grid with some of the 81 squares filled in with numbers.
Your challenge is to fill in the rest. There's only one simple, but often maddening, rule: The numbers 1 through 9 must appear only once in each of the grid's nine rows, nine columns, and nine 3-by-3 blocks. A proper sudoku has only one solution.
Where to start? Everyone has their own methods, but the following techniques - arranged from simplest to most complicated - should put you well on your way to unlocking even the trickiest puzzles.
Use a pencil
Pens are for pros. Even the easiest puzzles often require a little bit of scratch work that you will want to be able to erase as you solve squares.
Don't guess, only use logic
Proper sudokus have only one solution, meaning they can always be solved by logic. Don't place a number unless you have determined it is the only number that can go in that square. Trial and error guessing is hard work unless there are only a few squares remaining to solve.
Start with the most common numbers
Scan the puzzle to see which numbers appear most frequently. Pick one of those frequent numbers and see if you can easily place any more of them (there will be nine total).
The first time you try this, lightly draw lines crossing out every row and column that contains the number. Then look at each 3-by-3 block that doesn't contain the number already. If you find a block with only one empty space that isn't crossed out, place the number in the space.
In Example A, 8s are a common number. Lines are drawn through the rows and columns that already contain 8s. In two of the 3-by-3 blocks that lack 8s, only one space remains to put an 8.
Now try this method without drawing the messy lines, just scan the puzzle mentally Focus on rows and columns of 3-by-3 blocks where two out of the three blocks have the same number already filled in. The remaining block will contain the number in one of three possible squares - the other six are automatically ruled out as part of rows or columns that hold the other two instances of the number. Sometimes two of those three possible squares are filled or intersect a row or column that already contains the number you are trying to place. If so, you know the number can logically only go in the remaining square.
In Example B, two out of three 1s are already placed in columns. The remaining 1 must be located in the middle column of the middle 3-by-3 block. With only one empty space available there, the 1 must go where shown.
Move on to nearly completed chunks
As you start placing numbers, keep an eye out for rows, columns, or 3-by-3 blocks that are mostly filled in. When you find one, determine which numbers remain to be placed within that unit. Go through each of these unplaced numbers, checking to see if there is only one position within the unit where it could go.
In Example C, a 3-by-3 block contains seven out of nine numbers. The remaining two numbers must be a 3 and a 5. However, a 3 already exists in the middle row, meaning the 5 must go there and the 3 in the remaining slot.
Stuck? Start jotting notes
The easy "gimmes" have been filled in. Now your eyes are fixated on the page but your pencil hasn't touched it for a long time. You're stuck, meaning it's time to start working square by square, making small notes of the possible answers inside each. Pick a square and write down in tiny print any of the numbers 1 through 9 that don't appear in the square's row, column, and 3-by-3 block. By doing this, you may find a square has only one possible answer. Fill in the number, and cross out that possibility from other effected squares.
In Example D, the possibilities for each square in the bottom left 3-by-3 block are written out. One square has only one possibility - a 4. You can fill that in and erase all 4s from the possibility lists in that block, row, and column.
Look for overlapping options
Sometimes you will reach a point where all the unfilled squares have multiple possible solutions. Now the logic gets more complicated.
Your plan of attack is to find multiple squares within a row, column, or block that share similar options. For instance, if you can find two squares that have the same two options, those two numbers must be located in those two squares - and nowhere else within the rest of the row, column, or block, whichever it may be. This may whittle down the options in those remaining squares to a point where you can solve something else.
In Example E, the possibilities for each square in the top row of the puzzle are written out. Two squares have the same two possibilities - a 1 and a 4. Therefore, the 1 and 4 must appear in those two squares and nowhere else in the row. Erasing the 1 and 4 options within other squares reveals a square that can only be filled by a 9.
This trick also works when options overlap in more than two squares. As long as the total number of different options among a related group of squares does not exceed the number of squares involved, you can assume that each of those numbers resides somewhere within that group.
In Example F, the possibility are written out for all squares within the bottom row of the puzzle. Three of the squares share three common number possibilities - a 1, 4, and a 9. Therefore, the 1, 4, and 9 must be within those three squares and nowhere else within the row. After erasing the 1s, 4s, and 9s from the possibilities of other squares, one square is left with only one option - a 5.
Start over if you duplicate
Finally, if you find the number you have just placed is an illegal duplicate, stop and check the reasoning behind your latest placement. If the logic still holds true, start over. Erase everything, even if the puzzle is close to complete. You will not be able to easily untangle where you goofed - nor determine how many logical leaps sprung from that error.
Looking for Sudoku in the Monitor?
The Christian Science Monitor runs a new Sudoku every Friday in its printed edition, but due to production constraints, it is not available online.
You can subscribe to the Friday paper in print, or get a digital copy of the newspaper that you can print out yourself (and save 50%, too).
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