Now that we have some ways to describe the layout of a sudoku grid, we can start to build up the techniques needed to solve sudoku puzzles.
I intend to cover a specific method in each post but I will mark each one with a difficulty level so that you can jump in wherever you feel necessary. Along the way, I will be introducing more terms if we need them to describe a particular situation.
First up, then, is the “naked single”. Not a refugee from a dodgy dating website as you have guessed. No, this is a candidate that stands alone in a cell, with no other candidates to confuse you. It is sometimes the “last man standing” when you have done some other elimination and in easier puzzles there may be several of these singles right at the start.
How does this kind of candidate happen? We have to go back to the basic rule of sudoku for this. Remember that you can only have the numbers 1 to 9 once in each row, column or box. What that means is that the whole rest of the row has an influence on a cell which you are examining. Similarly for the column and the box containing it. In a simplified form, you could imagine this kind of effect taking place.
The cell marked X is aware of all that is going on in the area marked in green. Astrologers would love this, it’s like the influence of the planets. 🙂 The group of 9 numbers in a row (or column or box) is often called a “house” in sudoku and all the cells in the 3 houses that influence our cell are called the “peers” of that cell. There are 20 of these as you can see above.
Now let’s look at a real example. Here, I have marked the cells affecting 2,4 (remember row,column). If you look closely, you can see that all the numbers from 1 to 9 are present in the green shadow, except for 4. As a result, this is a naked single and we can immediately fill in the number 4 in our cell.
Once you have found a single, you can use the peers of that cell in reverse. This time, treat the cell as a miniature star radiating its number influence into the rest of its peers. If you are using pencilmarkings as we discussed in the last post, this will allow you to remove this number from the candidates in all those other cells. In fact, seeing these lines and boxes of influence will get you a long way into many puzzles as we use this idea again and again.
As a final piece of homework for today see if you can knock out any other naked singles in this puzzle.