Fillomino is a form of logic puzzle that was released by Nikoli. Nikoli has published 3 books entirely consisting of Fillomino puzzles by the year 2005. The game has also been referred to Allied Occupation in some instances.

Rules of Fillomino

A rectangular grid having no standard size is used to play the Fillomino game. Most of the time, the inner grid lines within the grid are dotted. In the Allied Occupation game published in World Puzzle Championship, Fillomino grid cells are circular. Some of the grid cells have numbers which are called "givens". The main goal of the game is to segregate the grid into a number of polyominoes in such a way that each of the given number n within the grid is a part of one n-omino and also that no 2 polyominoes of same size are orthogonally adjacent.

Contrary to some of the other contemporary puzzles of Fillomino, this game does not require a one to one correspondence between polyominoes and givens in the solution. Two givens having the same number can belong to the similar polyomino within the solution. It's also possible that a certain polyomino might have no given number at all.


Methods of Solving Fillomino

While trying to solve a Fillomino puzzle, it is a very common practice to add numbers in the empty cells if the size of polyomino each should belong to is determined. These numbers are associated appropriately to the givens. It is also made clear where the border segments has to be drawn, as for example, between any 2 differing numbers or around a region of identical numbers whose measure is represented by that number; it even helps to visualize the 2nd part of the rule of the puzzle as an identical number can't appear on both the sides of the border, and this really accelerates the solving of the puzzle. A very interesting side effect of putting numbers on every cell is after the puzzle is solved, these numbers alone can define the solution, while the actual borders are easily deducible. This allows for easy communication of the puzzle's solution without the use of a grid; in fact, the solutions for the puzzle of Allied Occupation are expressed by only the numbers.

The standard means of commencing a Fillomino puzzle involve drawing the borders between non-identical givens and also surrounding all the polyominoes that are completed only by the givens. From that point, the solver tries to search for 3 things, mostly possibly in a combination:

Potential overloads: If each and every polyomino within the solution were completely numbered, they would contain the subsequent matching numbers whose amount is represented by that number.

Limited domains: All the numbers within the grid, whether deduced or given, must be ultimately bordered in a region having that count of cells within it. Frequently a number will also need other cells near its region because of a lack of an alternate location for expansion.

Defined cells: Occasionally when the challenge is greater, it is easier to work with empty cells than with numbers. Most observable of these instances is when one single cell without any number becomes entirely surrounded; sans any help from any other numbers, that particular cell has to be a monomino. Hence it can be denoted with '1'.

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