TECHNIQUES FOR SOLVING FILLOMINO PUZZLES

The following presents the two fundamental strategies for the solving of FILLOMINO puzzles. Note that the successful application of a strategy always opens up new opportunities for one or both of the strategies to be applied again. This process should be continued until the puzzle is solved.

When specific cells need to be referred to, they will be designated as C4-R3 which means the 4th cell in row 3.

For a description of FILLOMINO puzzles, refer to  Building Fillomino Puzzles 

Strategy 1:- What if NOT?

 
This strategy involves the assumption that a particular cell does NOT have a certain value inserted into it. If this assumption leads to a logical inconsistency (typically, an invalid solution), then the original assumption must be wrong.

For example, assume that C3-R5 does NOT have the value 5 inserted into it. Then the 5 at C4-R5 can join with other cells to produce a zone with a maximum area of 2. This will not lead to a valid solution, so therefore our assumption must be wrong, and C3-R5 must in fact contain a 5. Similarly, C5-R3 must contain a 4, and C4-R3 must contain a 3. This is the strategy you will most often use. In fact some puzzles can be solved completely using only this strategy.

Strategy 2:- Only Choice.

 
Sometimes you will be able to identify a cell which can be filled in only one way. Look at C4-R1. If any number other than a 6 were to be inserted here, then additional cells could not be added to it to join it up with a similarly numbered cell without exceeding the zone area constraint. The same argument can be applied to C2-R1, C3-R1 and C3-R2.

Completing the Solution.

 
C5-R2 must be a 4 by strategy 1.
C3-R3 must be a 3 by strategy 1.
C2-R5 must be a 5 by strategy 1.
C2-R3 must be a 5 by strategy 2.
C1-R2 must be a 3 by strategy 1.
C1-R1 must be a 3 by strategy 1.
C5-R1 must be a 6 by strategy 1.
C5-R5 must be a 4 by strategy 1.
C2-R4 must be a 5 by strategy 1.
C1-R5 must be a 2 by strategy 1.

Astute solvers may find other, more obscure strategies which they can apply. However, the strategies listed here are guaranteed to solve any FILLOMINO puzzle created by Magnum Opus.