Solving Sudoku : Single Position
This is the easiest technique to apply by eye – and the one that most people use first when completing paper Sudoku puzzles.
Choose a row, column or box, and then go through each of the numbers that hasn’t already been placed. Because of other placements, the positions where you could place that number will be limited. Often there will be two or three places that are valid, but if you’re lucky, there’ll only be one. If you’ve narrowed it down to only one valid place where you can put the number… you can fill that number straight in, since it can’t go anywhere else!
Have a look in this puzzle at the green highlighted line:
Where could a 7 go in this row? We’ll leave the highlight in the cells that are empty:
Now look at any other placements which would stop some of the green cells.
Starting with the left hand box, there’s already a 7 right in the middle – that prevents us adding a 7 in our line if it is also in that box (marked in yellow). For now we’ll mark those cells in orange to show they’re not valid.
Looking at the central box – again there’s a 7, so that prevents a placement in the central box. Another placement ruled out!
There aren’t any 7s in the right hand box, but there are two 7s in the boxes top right and bottom right. They stop placements anywhere in their rows and columns. The bottom 7 doesn’t affect us – the only cell it could affect in our row is already filled by a 6, but the top 7 does prevent one of the cells being used.
So combining all of these together, between all of the other 7s in the grid, and the numbers already in our line, there’s only one place left for the 7 in our row.
And there we go – the final 7 in place! Just 51 more to place!
This technique is really powerful – and with some practice you don’t even need to have values in the line or use any kind of marks to see! Take a look at this puzzle – look to see where you might place an 8 in the middle row!
While sometimes you may end up having to scan every row, column and box, the chances of finding a single position are better in an area that already has plenty filled in.
Start your search in a line or box that is already busy, and you may save yourself quite a bit of time!
Sometimes this technique is referred to as a “Hidden Single” if the value is hidden alongside other possible candidates. You should still be able to spot it though!