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Description
The Hidden Single technique is one of the first things you will come up with when solving your first Sudokus. It is easy to apply and Hidden Singles are extremely frequent in Sudokus. In easy Sudokus you, oftentimes, need nothing more than Hidden Singles.
A Hidden Single is a single (a solution) that results from all other cells in that region (row, column, box) being blocked from that number.
Here is an example, where we will find a Hidden Single in the center box.
The 5 on the left prevents all cells in that row from being 5s because no two same numbers can be in the same row.
The other 5s prevent other cells within that same box from being 5s.
Now see how all cells but one in the center box cannot hold a 5?
This tells us that the 5 must be in that cell. (Because one region must hold every number between 1 and 9.)
Example from a game
Here, those 2s block most cells in the upper right box, so the 2 must go in the only cell that is not blocked.
Also columns and rows
While spotting Hidden Singles inside boxes is the easiest, they can, of course, also be found inside rows and columns.
Here, only one cell within the column can hold a 7. All other cells can see cells that have a single 7 in them.
When and how to look for Hidden Singles
Since Hidden Singles are the most frequent things you will find, you always start by looking for these. (besides Naked Singles)
To make the search for these more efficient, you generally want to prioritize three things:
- Start with the regions that have the least empty cells in them.
- Look at the numbers of which there are already a lot.
- Look for fixed numbers that affect many cells at once.
The first one can tremendously increase your solving speed, so you should definitely make this your habit. Always be aware of how many empty cells there are in each region (row, column, box) and focus on those.
In this example, there are only two regions that have four empty cells in them, so we look at them first.
In the bottom box, we cannot find a Hidden Single.
In the row, we find a Hidden Single, though, which is a 1.
We, then again, look at the region with the least empty cells. It is the same row in which we have just found the 1. But there is no Hidden Single left to find there.
So we continue with the next region that has the least empty cells. We've already looked at the bottom box, and the newly placed 1 does not help us there, but there is now another region with four empty cells. So we look at that.
And there we find another Hidden Single (3).
We now continue with all regions that have 5 empty cells and so forth.
This approach is, of course, no universal remedy, and there are with certainty many situations in which other approaches are more efficient, but it is a good guidance which brings you back on track should you notice that you are slowing down a bit.
When viewed from cell candidates' perspective
In later stages of the game, especially after you have executed some non-basic techniques, you will not necessarily be able to find Hidden Singles only by looking at fixed numbers in other cells.
That is, because non-basic techniques only remove one or more candidates from cells. So there might be a candidate missing from a cell, without there being another cell with a fixed number blocking that cell.
Here is an example.
See how in that blue region, only one cell holds the candidate 4? That is a Hidden Single.
But wait! There are only two of the five empty cells in that row influenced by other 4s in the grid. So what happened to the other cells? Why can't they hold a 4? There, the number 4 has been previously ruled out through non-basic techniques, and it only shows in the cell candidate pencil marks.
The result is the same, though. Every time there is a region where a number can only be in one cell, it is that cell's solution.