How To Solve Sudoku Puzzles

The first time you see a sudoku puzzle, you may get the impression that it is almost insolvable...

In reality, sudoku puzzles aren't quite that difficult; they can be solved with a little patience and logic.

Take a look at the following diagram:

Sample Sudoku Puzzle

We know that each of the nine subgrids or "regions" of three by three cells should contain every digit from one through nine.

That is true, for example, for the region in the top-right of the puzzle.

We also know that each digit may only be used once in every row and in every column.

This allows us to determine where the digit 3 should go in the top-right region:

Finding the first digit that can be entered in a cell

The first row of the puzzle already contains a 3 (in the top-left region). Therefore, that row may not contain another 3 (indicated by a red line).

Something similar is true for the second row, for it already contains a 3 (in the top-center region).

We now know that the 3 should be entered in the third (bottom) row of the top-right region; but in which cell exactly?

The cell in the middle already contains a digit (1), so we can't enter our 3 there; therefore, only the left cell and the right cell of the bottom row remain.

Next, we notice that we cannot use the right cell, because that column already contains a 3 (in the bottom-right region).

That leaves no other possibility for the 3 than the left cell of the third row! (Indicated in green.)

This provides us with some additional information, because there can be no other 3 in that column (indicated by the blue line).

Therefore, there are only two cells left in the region below that could contain a 3 (indicated in yellow).

We don't know yet which of these two should contain the 3, but solving other parts of the puzzle should give us enough information to choose the correct cell!

This puzzle (along with a link to its solution) can be found here.