by Elaine
(Midwest, USA)

I like Sudoku strategies that are simple and logical for me. I like solving Sudoku puzzles without using candidates, if at all possible. In reality, eventually you will need to put in candidates.

Step One

Find as many of the numbers (1 through 9) as you can, simply by looking at the placement of the given numbers in the puzzle.

I’ll use the Sudoku puzzle shown above to demonstrate what is logical for me. First, I look for numbers that are repeated often in the original given numbers. The completed Sudoku puzzle must have each number in the puzzle nine times (because there are nine columns and 9 rows).

You’ll see that the number 2 is given five times. So I look to see if I can determine where the other four 2’s should be.

You’ll see that column nine, row six has to be a 2 because columns seven and eight already have a 2 and rows four and five already have a 2.

You’ll see that column three row nine has to be a 2 because rows seven and eight already have a 2 and column one already has a 2.

Then you can see that column five, row two must be a 2 because columns four and six already have a 2 and row one already has a 2.

The last 2 needs to be in column two, row three.

I do the same thing for the 1,3,4,5,6,7,8,9 but cannot find any additional specific places for those numbers to be in this sample puzzle at this point in time.

Step Two

My next step is to try to complete the numbers in any column, row, or region where at least four numbers are known.

For this example, I will use the top one-third of the grid to demonstrate. That is, columns one through nine and rows one through three.

Row two has five known numbers. This means the other four numbers (5,6,7,and 9) are needed to fill the empty spaces in row two.

I start with the number 5.

I cannot conclude that the number 5 should go in column one, so I check if the number 5 can conclusively go in column two.

In row two, I already have 1,2,3,4 and 8. In column two, I already have 2,6,7 and 9. The only number missing is a 5. So column two, row two must be a 5.

We still need to place the 6,7 and 9 in row two.

In row two, there already is a 1,2,3,4,5 and 8. In column seven, we already have a 6, and in the top right region, we already have a 9. Therefore, column seven, row two must be a 7.

Now we need to place a 6 and a 9 in row two. The top right region already has a 9, so column nine, row two has to be a 6.

And that means column one, row two must be a 9. We’ve now completed row two.

We can see the top right region only has three missing numbers (1,4,5).

Column nine, row one must be a 1, because column nine already has a 4 and a 5 in it.

It is not possible, at this point, to determine conclusively where the 4 and the 5 should go.

So, we move on to the top left region because there are only three missing numbers (6,7,8).

You can see that column one, row three must be the 6, because there is already a 6 in columns two and three.

Now we have numbers 7 and 8 to place in the top left region. Column two already has a 7, so the 7 must go in column three, row one and the 8 must go in column two, row one.

Now that I have 12 additional numbers already filled in, I repeat the process.

Now there are six known 6’s, so I can determine that column eight, row five must be a 6 because columns seven and nine already have a 6 and rows four and six already have a 6. So you just keep continuing the process.

I hope this Sudoku strategy can help someone else become a pro at solving Sudoku.

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