BrainPuzzles

Hidden single

The first technique anybody learns, and the one that solves most of an easy grid: a digit that has only one place left to go in a row, a column or a box.

How to spot one

  1. Pick a digit and one unit: a row, a column or a box.
  2. Cross out every cell in that unit where the digit cannot go, because it already appears in that cell's row, column or box.
  3. If exactly one cell survives, the digit belongs there. It does not matter what else that cell could have been.

A real example

This grid is not a drawing. It came out of our generator, and the position below is one a solver actually reaches: every digit the reasoning uses is on the board, so you can check it yourself without taking anything on trust. The cells it looks at are green; the cells it changes are amber.

625173834739156274812385174746
In row 1, 7 has only one cell left it can go in. So r1c2 is 7.

Check it: in r1c2 the digits still legal are 4, 7, 8, 9. Everything else already appears in that cell's row, column or box.

The same move on a different grid

One example can be a fluke of the grid it sits in, so here is another, dug at easy from the seed second:hidden-single:100 with 30 starting digits. The technique fires in a different place, for a different digit, and the point is what it buys you afterwards.

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In row 5, 1 has only one cell left it can go in. So r5c5 is 1.

What the solver does next, from exactly that position:

  1. hidden single — In row 7, 3 has only one cell left it can go in. r7c5 takes 3, the only digit it had left.
  2. hidden single — In row 4, 3 has only one cell left it can go in. r4c4 takes 3, the only digit it had left.
  3. hidden single — In row 5, 3 has only one cell left it can go in. r5c3 takes 3, the only digit it had left.

That is the pay-off a hidden single is worth: not the one cell it names, but the run of cheap moves it unlocks behind it.

Where you meet it

Our grids are graded by the hardest technique they force, so a hidden single is what makes a easy grid what it is. Scan the boxes. No pencil marks needed. When you ask for a hint on one of them, the first thing the game says is the name of the technique and which row, column or box to use it in, and that step costs nothing — you still get to find the cell yourself.

The other techniques

Ready to use it? Play easy sudoku, take on the daily grid, or start from how to play.