## Posts Tagged ‘how to’

### Sudoku Gameplay and Strategy

Sunday, May 24th, 2009

### Objective

Sudoku is a Japanese puzzle game consisting of 9 rows and 9 columns, which when combined, create a 9×9 grid. This grid is then subdivided into 9 smaller 3×3 grids. The object of the game is to fill in each row, column, and 3×3 grid with the numbers 1 through 9. Each number can only be used once within each row, column, or 3×3 grid.

### Basic Strategy

One of the simplest ways of figuring out what number belongs in an empty box is when there is only 1 missing number in a row, column, or 3×3 grid. Figure 1

In Figure 1, the highlighted blue box, Ba, is the only empty box for row B. The only missing number for that row is a 4, and therefore, we know the blue box must contain it. This will also be the case for a column or 3×3 grid.

When there are two missing numbers in a row or column, those missing numbers cannot go anywhere else in their corresponding 3×3 grids. Figure 2

In Figure 2, Ac and Ic, the light blue highlighted boxes, are the only empty boxes for column c. The only missing numbers in the column are a 1 and a 3, so therefore they have to go in the two empty boxes. If you look at row I, you will notice there is already a 3, located in If. Since there cannot be more than one of the same number in a row, column, or 3×3 grid, the 3 cannot go in Ic and it must go in Ac. This forces the 1 to go into Ic.

This will also work if the box that is missing the number in a row or column is contained in a 3×3 grid that already holds one of the possible missing numbers (Ga). Another 3 cannot go in the 3×3 grid, forcing it to go into the other empty box in the row or column (Gh). This is further explained below. Figure 3

In Figure 3, row G is missing a 1. The two possibilities have been highlighted in light blue. The 3×3 grid that contains Ib already contains a 1, so therefore the highlighted box, Ga, is not allowed to contain another 1, even though the row that it is in still needs a 1. This forces you to put the 1 in Gh.

An easy way to start the puzzle before doing anything else though is to look at groups of 3 columns or rows. Figure 4

If you look at the top three rows in Figure 4, A, B, and C, the boxes Ae and Ca have a 1 already in them. The third 3×3 grid does not contain a 1. Because row A and C contain a 1 already, you know that the missing 1 has to go in row B. Because Bi is the only empty box in that 3×3 grid, the 1 must go there. If Bg and Bh, had been empty as well, you would have to look at the corresponding columns for that 3×3 grid. Columns g and h already contain a 1 as well, so the 1 must still go into Bi. This can be repeated for all columns and rows in sets of 3 and for the numbers 1-9. You may want to go through the puzzle twice, as you will find numbers and unlock possibilities that had not been there previously.

If you get stuck, grab a pencil and some paper. It’s often helpful to go through the puzzle and write down all the possibilities for each box. Sometimes only one number is able to go there. Figure 5

As in this case, the puzzle has been filled out so that all the possible numbers for each box are written inside in small print. In Ei, only an 8 is in the box. Therefore, that box must contain an 8.

In other cases, filling in possible numbers may lead you to a row or column with two boxes that have the same set of two numbers in then, with a third box containing one of those numbers, and another different number. Figure 6

Here in Figure 6, 2 and 8 are the only possibilities for highlighted boxes Fd and Fe. Fc has a 2, 8, and a 9, but because 2 and 8 are the only possibilities for Fd and Fe, 9 is left as the only possible answer for Fc.

Another example can be seen in Figure 7. Figure 7

Ab and Ac both only contain a 5 and 6, while Ad has a 5 and 9. You know that Ad can’t use the 5 since it has to go in Ab or Ac, thus leaving the 9 as the only number that can be put into Ad.

This logic also works when there are 3 boxes with 3 of the same numbers in them. Also, if after you have written down all the possibilities for each box, and within a column, row, or 3×3 grid there is only 1 of a certain number, you know that box will use that number, regardless if there are other possibilities for that box.
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As you spend more time playing Sudoku, these strategies will be easier to spot and you can move on to the super advanced puzzles. Good luck!