Tectonic singles

Most of a Tectonic puzzle is solved with singles. A single places one number with certainty, using nothing but the two rules.

The idea

Start from what a cell could hold. Its region’s size sets the range: a cell in a region of four cells can hold 1 to 4. Then rule out every number already placed in its region, and every number in a cell touching it, diagonals included. Two singles need nothing more: a region of one cell always holds 1 (Single-cell region), and a region with one empty cell left puts its one missing number there (Last digit).

Only number left

Only digit left. When a cell’s region and the cells touching it rule out every number but one, the cell holds that number.

The ringed cell at row 2, column 3 is in a region of three cells, so it can only hold 1, 2 or 3. It touches the 2 at row 1, column 3 and the 1 at row 2, column 2, so it must be 3.Bold numbers are given at the start and plain ones were placed by earlier steps. Small numbers are notes, and a crossed-out note is one the step removes. Shaded cells are the evidence, and a ring marks each cell the step is about.

In the example, the ringed cell at row 2, column 3 belongs to a region of three cells, so it can hold only 1, 2 or 3. The 2 directly above it, at row 1, column 3, rules out 2. The 1 to its left, at row 2, column 2, rules out 1. Only 3 is left, so the cell is 3.

Only place in the region

Only place in the region. A region needs each of its numbers once. When a number fits in only one of its empty cells, it goes there.

The four-cell region in columns 3 and 4 of rows 2 and 3 still needs a 4. Its cell at row 2, column 4 holds 2, and the 4 at row 4, column 4 touches both of its cells in row 3. The only place left for the 4 is the ringed cell at row 2, column 3.Bold numbers are given at the start and plain ones were placed by earlier steps. Small numbers are notes, and a crossed-out note is one the step removes. Shaded cells are the evidence, and a ring marks each cell the step is about.

In the example, the four-cell region in columns 3 and 4 of rows 2 and 3 still needs a 4. Its cell at row 2, column 4 already holds 2. The 4 at row 4, column 4 touches both of the region’s cells in row 3, one of them at a corner. The only place left for the 4 is row 2, column 3.

Try it

Easy puzzles need only these four singles. Play Tectonic, or go back to how to play.