How to Solve Norinori: Two Per Region, Dominoes Only

Norinori has no numbers on the board (they're shown above for illustration). The grid is divided into regions, and you shade squares so that:

1. Every region contains exactly two shaded squares.
2. Every shaded square touches exactly one other shaded square along an edge. Shaded squares come in pairs, like dominoes.
3. Two dominoes never touch along an edge (corners are fine).

The only clue is the shape and size of each region. A region of size 2 is the easiest case: both of its squares are shaded.

Deduction 1: small regions first

A two-square region is fully shaded, and that shaded pair is either a complete domino on its own or half of a larger arrangement. Either way, check what it forces next to it.

Deduction 2: finish the domino, wall it off

When a shaded square already has its partner, every other neighbor of both squares is unshaded. Mark them. Dominoes cannot touch, so each finished domino is ringed by safe squares.

Deduction 3: forced partners

A shaded square needs exactly one shaded neighbor. If only one of its neighbors can still be shaded (the rest are marked safe, or their region is full), that neighbor is shaded.

Deduction 4: full regions

As soon as a region has its two shaded squares, all of its remaining squares are unshaded. This is the fastest source of safe marks, so apply it after every move.

Deduction 5: count what each region has left

Once you have some safe marks on the board, count the squares in each region that could still be shaded. If a region still needs two shaded squares and exactly two candidates remain, shade both. If it already has one and only one candidate remains, shade that one.

The same count works on single squares. A square can only be shaded if it has a possible partner, so a square whose neighbors are all marked safe (or off the board) is safe too. Corners and edge squares run out of partners first.

Try a real one

This 6x6 was generated and checked by program: it has exactly one solution. Start with the smallest regions first.

Show the solution

Norinori is the newest of our three games and is now on the App Store.