# How to Solve Virtually Any Sudoku Puzzle

I was not a big fan of Sudoku at first but over time the unsolved puzzle next to my daily crossword won out. I was curious about its popularity and addictive quality, especially since I failed at so many half-hearted attempts.  A couple of years ago I sat down determined to solve one and I did just that.  It was not pretty; I literally forced myself to solve it with no strategy or system just sheer will of trial and error with numbers changed, crossed out, and every other mistake possible.

I had numbers in the margin, possibilities scribbled very tiny in each box, redrawn boxes out to the side and so on until it was done. Whew, but I did one, then another and another. It’s been a while now and I’ve done thousands of these puzzles and I guess I’m a bit of an expert.  Now I’m not perfect mind you, I goof plenty of them up, but it is usually just a careless error.  As for speed, I’m sure I wouldn’t win any contest or anything, but I can usually solve any newspaper Sudoku of any difficulty well under or around fifteen minutes.

When I say newspaper Sudoku, I mean any of the ones printed in the paper, usually having a difficulty rating of 2 through 5 out of 5.  Difficulty does not matter it just takes a little longer.  I’ve also noticed the puzzles rated 4 are the hardest for some reason. I have since purchased the paperback puzzle books and have found some of their more difficult ones to be complete stumpers, but can usually get through those if I lay it aside and come back to it later. However, the newspaper puzzles rarely pose this problem.

I have devised a simple system and it works nearly every time. I will list the steps I go through below. I have not included any charts or diagrams as I do not think it is necessary even if you are only vaguely familiar with the rules of the puzzle.  I will assume you know what those rules are without going into great detail; you know you must fill in the squares with the numbers 1 through 9 with no duplicates in any row or small box. Some of these steps may seem simplistic, but this system does work.

## How to solve Sudoku:

1. Either in order or backwards, starting with the first number that jumps out at you start filling in the numbers that are “givens”. That is to say with one number at a time look for and place it where it belongs in the squares where there is absolutely no doubt, question, or ambiguity as to it belonging there. Fill in all the “givens” you see, 1 through 9.

Now at this point you have a “new puzzle.” It is not the same puzzle you started with. Every number filled in is one less you have to solve. Always keep this in mind. On the easier puzzles you can continue this method by just going through the number sequences until the puzzle is solved. Once you’ve filled in all the obvious ones and looked for new obvious ones that have been created by you, you may hit your first wall. Now move to step 2.

2. Look over the entire puzzle as a whole and pinpoint different squares that appear to have a fair amount of numbers running in the same row both vertically and horizontally.  Mentally count 1 through 9 while your eyes scan each “plus sign/intersection” and inevitably there will be a few squares (the center of the plus signs/intersections) with all the numbers 1 to 9 except one (not the number 1, the ‘amount of one’ missing number).  This will allow you to fill in at least one or a few squares.  If you hit another wall. Move on to step 3.

3. Start with each vertical column and mentally run through the numbers 1 through 9 to see if one can be placed. This sounds time consuming or overly simplistic, but it goes really fast because some of the numbers are already filled in. Working one column at a time try to place the number 1 in every box of that column. You know the number belongs in a box if there is no other possible place for it. In other words if there are two “possible” squares for it, move to the next number, 2,3…  all the way through 9. Then do the next column and the next.

4. Use the exact technique in Step 3 only use it on the horizontal rows. These steps may seem futile at first because you will think you are not solving or filling in any squares, but it rarely fails, you will usually fill in at least 1 to 3 new boxes, again changing the dynamic of the whole puzzle. If you are not much closer to solving the whole puzzle by now you have hit another wall. Step 5 usually ices the puzzle and gets me “over the hump” on most puzzles.

5. Now look over the puzzle as a whole and look for rows, columns, and boxes with only three remaining blank. There should be a few. Now that you have found some areas that only have three remaining numbers as possibilities, determine what those three numbers are.  Pay close attention: Now one at a time (trying each blank box) look horizontally and vertically – IF TWO OF THOSE THREE DETERMINED NUMBERS CAN BE FOUND EITHER VERTICALLY OR HORIZONTALLY OR TOGETHER IN THE SAME ROW, IT IS THE THIRD NUMBER THAT IS NOT THEM THAT GOES IN THAT BOX. So by going around the puzzle and finding these rows, boxes and columns with only three needed, when two of those numbers share the row, you know they cannot be duplicated, so it is the missing number of the three numbers you determined to be needed.

Usually after going through Steps 1 through 5 I have all but solved the puzzle, it is just a matter of filling in the missing numbers that will be obvious.  If you are still at a wall, repeat the steps, as the puzzle has changed now by you filling in more numbers and, thus, will be able to fill in more by repeating the steps. On the rare occasion I have had to resort to step 6 which is hard to explain but it is rarely necessary.

6. Step 6 is a little like Step 5 except you look for rows, columns and boxes with only four needed to be filled in. Usually what you’ll find is not an overt one to fill in but you will be able to determine that two squares of the four squares must be this one or that one or be the spots for the remaining two.  You just don’t know which one goes exactly where, but you know, at least, they do not belong in the other two squares.  Now block them out mentally or with your thumb and look at the other two empty squares… there should be at least one that you can fill in this way.

These are my steps to solving the Sudoku Puzzles. Again, they may seem simplistic at first glance but if you follow them you will be able to solve almost any puzzle yourself.  It says there is no math involved in Sudoku, but I have to disagree a little because it is really process of elimination more than anything else and that is kind of mathematical.  It is also important to note that you never ever have to guess at filling in any box whatsoever.  It should always be without a doubt, 100% the only possible number to go in each box.

I was convinced early on you had to take a leap of faith and take a guess at some point in the puzzle and correct as you go.  As I’ve done more and more I realize that this is not the case.  Please share your comments or tips and let me know if you have any questions about the steps.  This is my main blog which I devote mostly to business marketing, but I just wanted to share my love of puzzles and offer these tips. Hope they help, have fun!

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### One Response to How to Solve Virtually Any Sudoku Puzzle

1. Michael Angel says:

Awesome tip sheet James! I agree it’s reason, not guessing that gets you ahead in this game. You should create add a bit more detail and market this as an e-book on Amazon!