"Hidden Singles" Technique

What is a "Hidden Single"?

"Hidden singles" is a quite simple Sudoku technique, but it requires careful attention from the player because it can be hard to spot.

The point of "Hidden singles" is that a Note (candidate) is the only one of its kind in an entire row, column, or 3x3 block, even though the cell itself contains other notes.

"Hidden" vs. "Obvious" Singles

• An "Obvious Single" (Naked Single) is a cell with only one note (e.g., {2}).
• A "Hidden Single" is a cell with multiple notes (e.g., {1, 7, 8}), but one of those notes (e.g., the '1') appears nowhere else in that block's notes.

How to Find a Hidden Single

It will be easier to understand this technique by looking at the example in the top-right 3x3 block.

In this block, we can see the following filled numbers and notes:

• Filled Numbers: 5 (R1C7), 6 (R2C7), 2 (R2C8).
• Notes (Candidates):

  R1C8 = {3, 4, 9}

  R1C9 = {3, 4, 9}

  R2C9 = {3, 4, 7, 8}

  R3C7 = {1, 7, 8} (Our highlighted cell)

  R3C8 = {7, 8, 9}

  R3C9 = {7, 8, 9}

Step 1: Scan the Notes for a Single Number

Instead of looking at a single cell, we must scan the entire block for a specific number. Let's hunt for the number 1.

R1C8? No '1' note.

R1C9? No '1' note.

R2C9? No '1' note.

R3C7? Yes, it has a '1' note.

R3C8? No '1' note.

R3C9? No '1' note.

Step 2: Find the Solution

The number 1 appears as a candidate in only one cell in this entire 3x3 block: cell R3C7.

Even though R3C7 also contains notes for 7 and 8, it is the only possible place the 1 can go in this block. Therefore, R3C7 must be 1.

We can now remove all the notes from this cell and put the number 1 in its place.

Master This Scanning Technique

That's it for the "Hidden singles" technique. Once you have learned it, you can proceed with the following Sudoku strategies.