Shared neighbour

A shared neighbour rules a number out of cells near a region before you know where that number goes. It is the step that Medium puzzles add to the singles.

The idea

A region needs each of its numbers somewhere. Suppose one of them can only go in a few of the region’s cells. Whichever of those cells it ends up in, a cell outside the region that touches all of them would touch that number, so it cannot hold it. This is Shared neighbour.

Example

In the example, the region at the right end of row 1 has two cells, so it holds 1 and 2, and both numbers are noted in each of its cells. Its 1 goes in one of those two cells. The ringed cells at row 2, column 3 and row 2, column 4 each touch both of them, one directly and one at a corner. Whichever cell takes the 1, it touches them, so the 1 is crossed out of their notes.

The two-cell region at the right end of row 1 holds 1 and 2, so its 1 is in one of those two cells. The ringed cells at row 2, column 3 and row 2, column 4 touch both of them, so neither can be 1.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.

Spotting it

Look for a number that is confined to two or three cells of a region that sit close together, often in a small region or at a corner. Then look for cells outside the region that touch all of them. Notes make the pattern easier to see, but the reasoning holds whether or not you have written them.

Play Tectonic, or go back to how to play.