Basic technique · 04

Hidden Single

Sometimes a cell has several candidates, but one number can appear in only one cell within a house.

BeginnerHouse-based

The idea

ONE CANDIDATE, ONE CELL.

A Hidden Single occurs when a particular number has only one legal location in a row, column, or 3×3 box. The cell may still contain other candidates, but that number is forced there.

The question: Where can this particular number go in this house?

Walkthroughs

LOOK FOR THE NUMBER, NOT THE CELL.

Hidden single is all about one number with one possible cell in a house.

Walkthrough

Example 01 — One place for a number

In the following example, cell r5c8 could have number 5 or 7 because all other numbers were placed in the row, column or box the cell belongs to; however, for column 8, r5c8 is the only place where 7 can goes to because if looking at its surroundings houses, box 9 has 7 paced, row 4 has 7 placed, thus cell r5c8 is the only cell left for number 7.

What to notice: The target cell may still have other candidates. The number is forced because nowhere else in the house can take it.

Placeholder for the example 01 — a number has one possible location in a house example puzzle screenshot

Walkthrough

Example 02 — Cross-hatching

Look at cell r9c2, number 1 and 4 could fit there because other numbers are already used in its row, column and box. Remember Scanning you just learnt? number 4 can only go to cell r9c2 of box 7 because after Scanning, 4 already takes row 7 and column 1!

What to notice: You are tracking one number through a house rather than calculating every candidate in every cell.

Placeholder for the example 02 — cross-hatching for a Hidden Single example puzzle screenshot

How it works

CHOOSE A NUMBER, THEN SCAN THE HOUSE.

Hidden Singles are about one number inside one house. This makes them different from Naked Singles, which begin with one cell.

CHOOSE A HOUSE

Pick a row, column, or 3×3 box that still has several empty cells.

CHOOSE A MISSING NUMBER

Focus on one number that still needs to be placed in that house.

SCAN ITS POSSIBLE LOCATIONS

Use the surrounding rows, columns, and boxes to eliminate cells. If only one cell remains, the number could be a Hidden Single.

A little history

A TECHNIQUE YOU MAY KNOW AS CROSS-HATCHING.

Hidden Single is a descriptive name for a basic Sudoku deduction. The idea follows directly from the rule that each number must appear exactly once in every row, column, and box.

When solving by hand, players often find Hidden Singles by cross-hatching: focus on one number and use existing placements to block its possible positions until only one cell remains.

Watch & learn

FOLLOW ONE NUMBER THROUGH THE GRID.

Comming soon...

Practice

FOLLOW ONE NUMBER AT A TIME.

Choose a number and a house. Block its impossible positions and see whether one cell remains. Repeat with another number.