A practical guide to numbered Fillomino regions

Fillomino combines a jigsaw partition with a simple arithmetic rule. Every cell belongs to one region, and every region is connected through shared sides rather than corners. The number attached to a region equals its area: a 3 region contains three cells, while a 5 region contains five. Two separate regions with the same number cannot share a side.

Numbers and regions supply different information. A printed clue fixes a region’s size but leaves its shape open unless borders are drawn. A border says which cells must stay together, while the clue limits that group’s area. Some editions show only clues; others include partial or complete outlines. Mixing up these clue types can lead to false deductions.

The task is not to fill every square with an arbitrary digit. It is to place region boundaries so each group has the correct area and obeys the adjacency rule. Read both the numerical and spatial constraints, and the puzzle becomes a sequence of manageable eliminations rather than guesswork.

Separate numerical clues from spatial clues

Circle each number and note its value. A solitary 2 can only be a horizontal or vertical domino. A 3 may be a straight bar or an L shape, while a 4 can form any tetromino, including square, T, L and skew forms.

If an outline encloses a numbered group, count its cells at once. Four cells with a clue of 4 confirm that region; three cells with a clue of 4 show that it must expand by one. Never cross a solid region line while seeking that extra cell.

Survey the whole grid before extending

Look for the most constrained clues first: a number boxed in on three sides, a tiny outlined region, or a 1 with no free neighbour. Treat these as anchors. Equal-number clues close together are also useful because their regions have fewer safe growth directions.

Sketch candidate shapes lightly in the margin or use symbols in the cells. Distinguish cells that must belong to a region from those that merely might. This prevents a plausible extension from becoming an accidental commitment, particularly on a crowded 10 by 10 grid.

Grow each region one cell at a time

From an anchor, add only cells that keep the group side-connected. For a 3, the candidates are a three-cell strip or three cells forming a corner. If one direction is blocked by a border or the grid edge, the corner version may become the only possibility.

Check after every addition. The moment a candidate reaches its clue value, it must stop; a path that would create a 4 around a 3 clue is invalid. Do not merge two clues of the same value either, because their numbers belong to separate regions that must remain apart.

Use borders as powerful shape filters

A drawn boundary removes more possibilities than the number alone. A 4 clue surrounded on three sides by walls may have to stretch in the remaining direction, but it must still form an allowed tetromino. If that route creates a disconnected or wrongly shaped group, reconsider the boundary.

Region lines also show where no boundary may be placed. If a numbered area already contains the required number of cells, seal it mentally and solve around it. If it is short, locate the missing cells nearby. Borders are constraints, not decoration.

Keep equal-sized regions apart

The same-number rule can break a stalled solve. Two 3 regions cannot touch side-to-side, although diagonal contact is allowed. When equal-number clues are separated by a narrow corridor, restrict their outward growth so the finished regions cannot become neighbours.

A candidate 3 extending towards another 3 is not automatically wrong if both can be reshaped, so test alternatives rather than banning the entire area. Only the completed regions, not every intermediate pencil mark, must obey the separation rule.

Count remaining space and test contradictions

When direct placement is difficult, count the unfilled cells around a region. If a 4 region has three confirmed cells and only two empty cells remain nearby, one must be chosen. If only one is available, the shape is fixed.

A 1 region is always a single cell, so every side-neighbour needs another value. In a two-by-two block, three cells assigned to one 2 region are impossible because they form an L rather than a domino. On larger grids, shade candidates by region, erase any extension that exceeds the clue size, and reject a region with no possible growth path. Work backwards from the tightest area to loosen broader placement.

Build a routine for Australian puzzle days

A dependable sequence is to read all clues, count existing region cells, fix small or enclosed regions, extend candidates, and check equal-number adjacency. Use pencil, keep a clean candidate layer, and spend the final minutes verifying every region’s size and connectivity. Short sessions suit beginners; larger grids benefit from a fresh second look.

Fillomino fits local habits. It can fill an arvo break in Melbourne with a flat white on the table, or a quiet stretch on a Sydney suburban train without filling the carriage with paper. Puzzle fans browsing an Australian bookshop or the puzzle shelves at Officeworks and JB Hi-Fi may find Sudoku collections, specialist journals and occasional Fillomino titles.

Many Australians also protect puzzle time around major sporting weekends, including the AFL Grand Final, when a compact grid is easier than a long puzzle book. Zagonetka.net links that habit to Croatian and international logic-puzzle news, schedules, results and practice material. Each number sets an area, each border limits a shape, and every completed region must satisfy both constraints at once.