Sudoku

Are you in need of a few hints on how to solve Sudoku Puzzles?  Or maybe a logical method of even approaching a Sudoku puzzle.

My method is to first eliminate the obvious solutions and then attack the less obvious solutions that require a more complex approach.  This puzzle for instance.

The first thing I do is look for the obvious solutions starting with the number 1 and ending with 9.

See, in the third middle square, I determined that a solution was to place a blue 1 in the position shown.  This is the only number that can go in that position.

The blue 2, is the only number that will fit in that position.

The blue 4's are the only numbers that will fit in the positions shown.

The first blue 5 in the lower right square was determined by the lower left square.  The bottom row in this square has to have a 5 as determined by the other positions not being able to have a 5.  This eliminates having a 5 in that row in the other two squares to the right of it, leaving only one position eligible for the number 5 in the lower right square.  This 5 in the lower right square, shows that another position in the upper right square is eligible for a 5


6's are determined the same way.  the two 6's in the lower left and the lower middle, shows one position in the lower right elgible for a 6.  The 6's  in upper middle and lower middle show that a 6 goes in the middle middle square as shown.  The 6's in the upper left and middle upper, show a 6 in the upper right square.  The 6 in the upper middle eliminates all but one position in the middle middle square. And so on.
 
Now we can look for obvious solutions outside the box.  The first thing to do is look for nearly complete solutions such as a column with only two numbers missing (8,9) for instance.  Then by observation, you can tell that an 8 has to go in the lower right square (which already has a 9), leaving a 9 for the upper right square.  All of the shade of grey numbers were determined in this fashion until not being able to progress any further.

What's left, is to try to find another singularity by observing the possible solutions for the remainder of the puzzle as shown by the small red numbers.  The rows and columns and squares with the least open numbers are done first.  This may go on for quite a few numbers or if you are lucky, a few numbers until a singularity is revealed.  Notice for instance in the upper left square, the numbers 8,9 are unique to those two positions and cannot contain any other numbers in those two positions leaving the missing numbers 2,7 for the remaining two positions.  It is important to remember that when two numbers exist like this, they can be used as part of the solution as well.


The green numbers are a result of finally finding a singularity by the above method and then leveraging this to determine the next number.  The above puzzle is nearly complete and easily finished.

To check if your solution is valid, look for and determine that each row and column do not contain any duplicate numbers.  You can also wait for "tomorrow" to get the solution to "yesterdays" puzzle (boring).

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