First moves

Almost every Fillomino puzzle opens with the same three deductions. Learn to spot them at a glance and the first third of any board solves itself.

1. A complete region is walled off

As soon as a region reaches its size, it is finished. No neighbouring cell can hold the same number, because it would join the region and make it too big.

Two 2s side by side are already a finished domino, so the cell to their right is not a 2.

The most common case is the 1. A clue of 1 is complete from the start, so none of its four neighbours can be 1. On a board with many 1-clues, this alone removes a lot of possibilities.

Get into the habit of mentally drawing a wall around every finished region. The walls are what shape the rest of the board: they block regions from growing, and they create the enclosed pockets covered in the next article.

2. Two clues that would merge

Look for two clues of the same number with one empty cell between them. If that cell took the same number, it would connect both clues into a single region that is too large.

Filling the middle with 2 would make a region of three 2s, so it must be something else.

The same idea works for bigger numbers. Two 3-clues separated by one cell can't both reach through that cell; filling it with a 3 would make a region of at least five. Whenever you see matching clues close together, ask whether they belong to the same region or to different ones. If the clues are touching, they are in the same region. If the count doesn't fit, they must be kept apart.

3. The only way out

A region that still needs to grow must grow through one of its empty neighbours. When only one neighbour is available, that cell must take the region's number.

A 2 in the corner, blocked on the right by a 1.

The only way out is down. With the domino finished, its new neighbours can't be 2.

Here the 2 sits in the corner of the board. Above and to the left is the edge, and to the right is a 1, which is finished and can't be joined. The only empty neighbour is below, so that cell is a 2. That completes the region, so you immediately apply rule 1 again: the cells next to the new domino can't be 2.

This is how Fillomino logic usually flows. One forced cell completes a region, the completed region walls off its neighbours, and those walls force the next region. Corners and board edges are the best places to look, because a region there has fewer directions to grow.

Putting it together

When you start a new puzzle, scan the whole board once for each of these patterns in turn: finished regions (especially 1s and pairs of matching adjacent clues), matching clues that would merge, and regions with a single way out. Fill in everything they give you before doing anything clever. On easy puzzles that is often the whole solution.