How To Solve Fillomino Puzzles
Each puzzle consists of a square grid with some squares containing a single digit number. Place numbers in the blank squares (horizontally and vertically) to divide the board into blocks. Each block contains as many squares as the number provided in the block. The puzzle can provide two or more of the same number in a single block. Blocks can take any shape, but blocks having the same number of squares may not touch each other.
Here is a typical Fillomino puzzle grid. The grid size can be smaller or larger and varies in difficulty.
The puzzle requires that you place numbers in the blank squares to divide the grid into blocks the size of the corresponding number provided.
For instance, in the sample puzzle above, the 4 in the first row indicates the block it belongs to is four squares in total. This block can be any shape expanding horizontally and vertically. Remember that two different blocks with the same number of squares cannot touch.
The solution to the puzzle is shown here.
Notice that each blank square is filled with a number corresponding to the original number provided. The groups of the same number reveal the blocks.
Some Common Strategies
Look for the 1's. Since the squares containing a 1 can only have 1 square in the block, they are each an entire block and can be highlighted. This may help to discern surrounding blocks better.
Look for squares that have their shape forced. For instance, in the example above, there is a 5 in row one and another directly below it in row two. The configuration of the other numbers around it tells us that the squares to the left of both 5's must be a five. The block cannot extend to the left any further because it cannot block the 6. Since we now have four of the required squares in this 5-square block, the only square left available is the one to the right of the 5 in row 2.