Solving Sudoku Part 2

This is the second in a series about the Sudoku puzzle and some of the solution methods. In the last post the puzzle was defined and the rules for solving were shown. In summary, you have a 9×9 array of squares that have to be filled with numbers such that each row, column and container contain one through nine with no repeats.

In this post we’ll show the method to find the “gimmies,” or numbers that you don’t really have to think very much about. Let’s recall the puzzle…

Sudoku puzzle as you might find one in the newspaper or a book.

Recall the container rule that every container must have the numbers one through nine in it. Given that, consider the top three containers which form a group of three rows. Look for two of those containers having the same number in them. Sometimes this combination will define a unique place for that number in the third container. Let’s see an example of where that happens in this puzzle…

Illustration of a Sudoku gimmie.

The first two containers have the number 4 and the third does not. Now, look at the rows that contain those 4’s. Look at the yellow lines that cover those rows. What they mean is that the number 4 in the third container cannot be in either of those two rows. That would violate the no repeat rule. Since there is a given number in one of the three top squares in the third container that leaves two empty places where a 4 can go. If you now look at those two columns you will note a 4 in the one on the right (covered in yellow). That leaves exactly one (the red square), and only one place where a 4 can go in that third container so you know you can fill it in. It doesn’t matter what other numbers might be able to go there, you know by this technique that they don’t matter. Only the 4 goes there. Congratulations. You’ve now entered your first number into the puzzle and you know it has to be correct!

Let’s do it again. Look at the following image to see the next number you can enter into the puzzle…

A second gimmie in the same puzzle.

This time we’re looking at the two 8’s in the first two rows of the top containers and the two empty spaces in the middle container where an 8 could go. By exactly the same logic the 8 must go into the square marked in red. Good show! You now have two squares filled in.

Now you try. Move to the middle row of containers and see if you can find any gimmies (hint, there is one). Then, move to the bottom row of containers and look again (one again there). When done with that you should have four total squares that have numbers as shown here…

All horizontal gimmies in the puzzle.

Now, as you might expect, the next step is to do the same thing with vertical columns of containers. As it turns out there is only one vertical gimmie. It’s a 1 and its location is shown here in the red square…

First and only gimmie found with a vertical search.

When you have determined the location of any vertical number be certain to take a second look at the horizontal containers for that number. It may duplicate another in that row of containers and give you an additional entry in the puzzle. This puzzle has none of those but the easier puzzles will often have several.

Note: It’s important when finding the gimmies to stay within the containers. Do NOT pick three rows at random and attempt to use them to find gimmies. Picking, for example, rows 5, 6, and 7 would not give valid results even it it does yield a number. Eventually you would run upon a duplicate in a row, column, or container and have an invalid solution.

That’s it for the gimmies. You have now added five correct numbers to the puzzle. The next post will cover what to consider next.

 The Series