Solve a Sudoku

Sudoku is a numbers puzzle that has swept the world. It is very fun to play, but can be tricky and confusing at first. The objective of the puzzle is to put the numbers 1-9 in every row, column, and 3x3 square block.

Steps

Easy Difficulty

  1. Understand the rules. Each row, column, and 3 by 3 square must have the numbers 1 through 9. These numbers can't be repeated in each row, column, and square. Certain Sudokus will specify if the diagonals also must have the numbers 1 through 9.
  2. Seek "definites". When solving an easy Sudoku, the first thing you should do is look for definites. Definites are numbers that are definitely going to be there. Starting at 1, draw imaginary lines through boxes in that 1's row and/or column. When there is only one box left in the 3x3 box, you know that is a definite. (See images one and two.)
  3. Work your way through the numbers until 9. Since you have filled in some numbers, this should help get other numbers that had more than one possibility before. (See images three and four. Notice how the 3s could not have been solved before, but are solved in the final).
  4. Look again when stuck. If you get stuck, go back and make sure to look at everything. It is almost guaranteed you missed something. That one number is usually all you need to get going again. If you still cannot find any solutions, start labeling every block with every number that could possibly go in that box.
    • For example, in image one, all the empty boxes have numbers that could possibly go there. Fill these in. If there is a 1 in the row or column of that box, you know that 1 is not a possibility.
  5. Start by doing Sudoku in the newspaper or online (see links below). The newspaper sudokus are usually easier on Monday and Tuesday. The difficulty increases as the week passes.
  6. Try your hand at harder Sudokus. This particular Sudoku (images one through four above) could be solved with only definites, but what do you do if it can't?

Hard Difficulty

  1. Start at number 1. Use the same logic from an easy puzzle to fill in every empty box with all of the possible numbers for that box. If possible, put in definites. For example, picture three (above) shows that you can't solve for 3.
    • In a hard Sudoku, you won't be able to solve from the start, so just fill in what you know it could be. This will help later when you have two or three options per box and you can't remember what they are.
  2. Note that if two boxes in a block, column or row must be one of two numbers, you can use those numbers to eliminate other possibilities. For example, in a block, there are four open boxes. From your analysis, you have determined that:
    • box A can be 1, 2, 3, or 4;
    • box B can be 1, 2, 3, or 4;
    • box C can be 3 or 4; and
    • box D can be 3 or 4.
      • From this we know that box A and B cannot be 3 or 4, because they have to be either 1 or 2. Box C and D have to be either 3 or 4. This information might be useful in solving other boxes.
  3. Recognize that hard Sudokus can take time - a lot of time. A hard Sudoku can actually take days to complete, but they are still fun. The harder they are, the more fun it is when you finish. A hard Sudoku can be solved the same as an easy one, it just gives you less to start with. The logic of a hard puzzle is that if you know everything that can go in every box, it is very simple.
    • For example, say you have two possible 2's for a particular nine-square box, and they are in a row or column and you know that 2's cannot go anywhere else in the nine-square box. This means that you know that the row or column those 2's are in cannot have 2's in it except in this nine-square box. This sounds confusing, but when applied, it is actually very easy and it helps a lot.
  4. Consider this alternative, surefire way to always solve a puzzle accurately and quickly. In this method, fill in each block with all the possible numbers that could go there. Write all the numbers small at the top of the block. You can recreate the puzzle on bigger paper to help with this. Write all the numbers that don't appear in that row, column or square. Once you have done this for a whole column or row, start filling in the obvious answers. You will have solved the puzzle by the time you do this for every row.

Samurai Sudoku

  1. Be a confident and advanced Sudoku player. The Samurai Sudoku puzzle is a puzzle only to be attempted by a skilled Sudoku solver. It is basically five Sudokus in one. The corners of each are interconnected with a middle puzzle (see image below). These puzzles can be long and difficult.
  2. Keep the connections in sight. When solving these, you must always remember that the corner connected with the center puzzle must work with both puzzles.
  3. Look at the lines. The lines that are twenty-one boxes long are going to be looked at as if there were three separate nine block lines, one of which is comprised of pieces of the other two.
  4. Solve just as you would a regular puzzle. Just remember that you can have up to three of the same number in lines that connect to the center puzzle.

Killer Samurai Sudoku

  1. Take a look at the killer variant of the samurai Sudoku. The rules are a bit different, and the grid now involves color. The standard Sudoku rules apply to this puzzle as well, i.e. each nine square box has to have the numbers 1-9

Killer Samurai Rules

  1. Look within each of the colored blocks for a small number. This denotes the total value of the squares within that block. For example, if a colored block comprising 3 squares totals 7, then the individual squares must be 1, 2 and 4, but it is down to the reader to ascertain in which order they must be placed.
  2. Notice that within each colored block, a number may be repeated, although this is rare.
  3. Note the total. Each nine square block must total 45, as must every row and column.
  4. Realize that in a Killer Samurai puzzle there are 4 instances where 3 x 3 grids belong to two different nine square blocks. In this situation the same rules of Sudoku apply, i.e. the numbers 1 – 9 must be used once only. It stands to reason that these 4 grids can hold the key to solving the entire puzzle.

Advice for Solving the Puzzle

  1. Look for colored blocks which contain high or low totals. These have fewer combinations of numbers and are, as such, easier to solve.
  2. Look for a group of colored blocks which protrude beyond the boundary of the nine square blocks by one square only. This will allow the reader to determine at least one square of a colored block.
  3. Don't just think of a single block totaling 45. It may sometimes be possible to ascertain a number by adding colored blocks in 2, 3, 4 or more nine square blocks totaling 90, 135, 180 etc to ascertain a single elusive number.
  4. Look for intersecting colored blocks with high or low totals. For example, where a colored block totaling 3 is at 90 degrees to a colored block totaling 4, the values of the blocks should be easy to work out as there is only a choice of 3 numbers; 1, 2 and 3, but don`t forget that each row and column must contain the numbers 1 – 9 once only.
  5. Look to eliminate 'pairs'. If a colored block of 2 squares totals 4, 6, 8 etc., logic tells you that the numbers contained within cannot be 2 & 2, 3 & 3 and 4 & 4 etc. thus reducing the permutations.
  6. Look for colored blocks that form 'lines'. For example, if 4 colored blocks of 2 squares form a line, then the missing number can be calculated by deducting the total from 45.

Number Combinations

  1. Be aware of 2 square combinations. These include:
  2. Be aware of 3 square combinations. These include:
  3. Try less advanced Sudoku before moving on to Killer Samurai Sudoku. Killer Samurai Sudoku is an advanced variant of Sudoku and it is highly recommended that you try to complete a normal and also Samurai Sudoku before undertaking these more complex puzzles. These are extremely hard puzzles. They may take days to complete. Just have patience.

Sample Sudoku Puzzles

Doc:Easy Sudoku,Intermediate Sudoku,Hard Sudoku

Blank Sudoku Template

Doc:Blank Sudoku



Tips

  • Another good place to practice your Sudoku skills is in a book. There are many books with Sudoku puzzles in them. Some even have step by step instructions to improve even more.
  • Copy the puzzle onto a grid much bigger than the ones in the newspaper, using a marker. Now solve the puzzle using the bigger squares to clearly write in pencil all the possible numbers.
  • Try to find the obvious first.
  • Have contests with your friends or coworkers. Make copies of a puzzle and try to see who can finish the fastest. Doing this once a day or once a week will help to dramatically increase your speed.
  • Go by box, then by row, then column.
  • Check twice, put a number once.
  • Instead of writing numbers, imagine each square as a 3x3 grid of dots. A dot in the upper right corner is a 3, one in the middle is a 5. This method involves less clutter in each box.
  • Your speed increases with regular practice.
  • Use the web-pages below to help you. They are all very useful, but try to stay away from the auto-fillers. Where is the fun if the computer does it all for you?
  • If you're having a block, stop, and take a break for a couple hours. Take a nap, do some errands, play a game, etc.
  • Sudokus are also fun and exciting to make. Making them can also increase your skill at solving them.

Warnings

  • Before using solvers, try to solve it yourself. Where is the fun if something else solves it for you?
  • For every cell you fill in, make sure you double, or even triple check your logic; one single error could mess up the entire puzzle. If you are almost sure a three can go in a box, triple check why you think this. If there is even a remote possibility of a three going in a different box, don't put a number down! Many a person has almost finished a puzzle only to find that they put one number in the wrong place.
  • It is considered cheating if you guess at where a number could be. All true Sudoku puzzles are solvable with only logic. If there are two possible numbers that could go in a space and you just choose one and hope it's right, this is cheating.
  • Try to look at the puzzle both ways; rather than working north to south all the time, try east to west. Remember, it's always a good idea to look both ways before crossing the street.

Things You'll Need

  • Time
    • 10-20 minutes for easy to medium after you've become a little experienced.
    • 30-45 minutes for medium to hard.
    • 1-4 hours for Samurai (unless you are very skilled).
    • 4 hours+ for Killer Samurai
  • Pencils
  • Erasers
  • Patience
  • Logical ability

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Sources and Citations

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