Fillomino...

In my mission to post about as many different unusual puzzle types as possible (or so it seems - I just love the variety) then I thought I would write about another of my faves for anyone who hasn't come across it before.

The puzzle is called FILLOMINO. According to wikipedia this is also sometimes called allied occupation though I've only ever seen it called fillomino. I came across it once when I bought a little book of the puzzles when on holiday in France of all places. I've never seen it back home though I don't think.

Anyhow fillomino is, if not unique, quite rare, in that it is a puzzle whereby all the regions are not necessarily given to you at the start. This means you can get some really fun 'reveals' whilst solving the puzzle which you don't get elsewhere. I'll try to explain!

In fillomino the grid, often square but certainly rectangular, contains some cells with numbers in, like say sikaku. Then, you have to work out what region each of those cells belong to with each number belonging to a region containing that number of cells. However, unlike sikaku, the regions are not necessarily rectangular, and in fact usually they are not.

Also, numbers of the same value *can* belong to the same region (poly-omino) so again here there is an interesting piece of logic about working out whether givens of the same value that are 'within reach' of each other must belong to the same or disparate regions.

My favourite rule is that it is not necessary for at least one digit from each solution polyomino to be stated in the start of the puzzle. Using the sikaku analogy again, in that puzzle you never need to add in new rectangles, what you see is what you get (the sum total of the numbers in the sikaku grid is therefore the same as the number of squares in the puzzle), but in fillomino this is not necessarily the case... and even if it is, there could still be new regions to add if any givens of the same value are in reach.

Anyway this makes the puzzle really enjoyable, because sometimes you get really nice new regions that are forced upon you by the way the puzzle solves, for instance in that little book I mention above there was one memorable puzzle that I think was only 6x6 (possibly 7x7) but still forced a new region to be created of size 7: none of the combinations of regions of size 1,2,3,4,5,6 were valid due to the fact that no two regions of the same value can have any cells that are horizontally or vertically adjacent.

Anyone else played fillomino?

More to the point... any chance of getting a collection of fillomino puzzles on here if I ask nicely?!

Re : Fillomino

I think I have played it once on an online puzzle collection. I don't seem to remember that there was the rule about adding new regions though - or perhaps I just didn't have to do it.

I did a few puzzles from the player and they were all I have to say very simple indeed so it could just be that I didn't come across any of the more interesting rules you mention.

I do enjoy some of those interesting puzzles that are just so hard to find elsewhere so certainly I would be pleased to revisit it and try some more fillomino if such a collection were to become available on here!

Re : Fillomino

Hi Martha

I think I know the one you mean, I think it is called filling on that tool.

I would say that you can't complain because it is free, but those are "fillomino light" puzzles, by which I mean they only have a couple of rules required to solve so any interesting puzzles that use the full range of fillomino logic and require different combinations to be considered etc never occur: so they are all very simple to solve. That's fine for beginners but it means you don't ever get the nice solving experience that a good fillomino puzzle can give you.

I can imagine it is a real stinker to create because of the fact there are so many considerations: the fact that you can add the new regions must mean there are loads of possibilities for a generator to come up with. They also will need to presumably work out the different options for each of the polyominos that make up the puzzle: there are algorithms out there to generate these from the links I've followed on the wikipedia page on fillomino but I guess that again makes it a lot harder to create fillomino compared to, say, the good old sudoku puzzle!

Re : Fillomino

Ah, that probably explains it!

Yes, I did the ones with that tool you mention. As you say it is hard to moan about it as it is free to play, but if real fillomino puzzles as you put it are much better than that then its a shame it creates a negative impression of the puzzle!

Having been encouraged to look more widely, I found another site that had a small number of, just ten or so I think, and I found it indeed to be a completely different kettle of fish: much more fun to solve and some good discoveries where you had to create additional regions and some of them were surprisingly large... now that I know that fillomino if created properly is actually a good, fun puzzle then I will try and seek out some more, so a collection here would be most welcome!

Re : Fillomino

Great post, that's a very clear description of fillomino!

It also happens to be one of my favourite puzzles; I can't remember seeing it published in a UK puzzle magazine / puzzle collection before but of course I haven't seen anything like all of them so can't be sure. But suffice to say it is, at least, a particularly rarely seen Japanese puzzle.

As you rightly say they are hard to create and can therefore take a long time to do so. Adding or removing one number to a puzzle can be the difference between making a puzzle unsolvable and trivial just due to the vagaries of the rules. Therefore it can be particularly time consuming to write fillomino puzzles!

Re : Fillomino

Hi puzzlemags

Just realised that I never replied on the fillomino puzzles.

I can see that they would take a long time to create so it might not be practical to create a magazine of these unless there was more demand.

However perhaps if, as mentioned elsewhere, a 'variety puzzles' magazine was created of the various puzzle types then a selection of fillomino puzzles could be included in it?!