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?! 
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