Fillomino is a puzzle originally from nikoli; you can see their description of the puzzle here. The object is to fill every grid cell with a number; some will be provided. If one were to draw boundaries between every pair of adjacent squares except those with the same number, partitioning the grid into polyominoes, then each number should tell how many cells are in the polyomino that contains it. The solution is unique.
Below is an example puzzle and its only solution.