Everydoku

Hidden single

The naked single asks “what goes in this cell?”. The hidden single asks the opposite: “where does this digit go?”. Even when a cell still has several candidates, if a digit has nowhere else to go, that cell is the answer.

Why it works

Every box must contain each digit from 1 to 9 exactly once, and so must every row and column. So if you rule out the empty cells of a box one by one for the digit 9 and only one cell is left, 9 has to go there, however many other candidates that cell has.

On a real board

Where can 9 go in box 1? The lines from the orange 9s (hatched) block every other empty cell of the box, leaving only the blue cell. Play this board →

This is the starting position of a 9×9 · Normal board. There is no 9 in box 1 yet. Where does it go?

  1. Find the 9s on the board. Each of row 2 and row 3 already holds a 9, so no cell of the box in those rows can take 9.
  2. There is also a 9 in column 2. Rule out the box's cells in that column too.
  3. Only row 1, column 3 is left. It is the only place for 9 in the box.

Looked at on its own, that cell has several candidates, so a naked single would not find it. You only see it by scanning the box for one digit. That is why it is called “hidden”.

Cross-hatching

The classic paper method is cross-hatching.

  1. Pick a digit. The more often it already appears on the board, the better.
  2. From each cell holding that digit, draw an imaginary line along its row and column. The hatching in the picture shows these lines.
  3. Look for a box without that digit where only one empty cell is free of lines.

When you have swept the board for one digit, move to the next. One round from 1 to 9 usually fills a few cells, and each new digit narrows the places for others.

Rows and columns too

Hidden singles are easiest to see in boxes, but they work the same in rows and columns. If a row has three empty cells and two of them sit in columns that already contain a 4, the row's 4 goes in the third cell. When a row or column has only two or three empty cells left, ask for each missing digit which of those cells it can go in.

Watch the counters. In Everydoku, the small number under each key on the number pad shows how many of that digit are still missing from the board. Digits with one or two left are nearly placed and make a good place to start looking for hidden singles.

Where you need it

9×9 Normal, 6×6 Normal, 12×12 Normal and 16×16 Normal boards were chosen so that this technique is required: naked singles alone get stuck halfway. Alternating between the two techniques takes most boards a long way.

When you can see neither, it is time to write down what each cell can still be. Continue with pencil marks.