Fillomino: Divide the grid into regions of orthogonally-connected cells such that no two regions of the same size (ie with the same number of cells) share an edge. Enter a number into each cell equal to the size of its region. Four Colour Theorem: Each region must be shaded entirely in one colour. There are a total of four different colours in the grid. Regions of the same colour cannot touch orthogonally. Additionally, regions of the same colour must be of different sizes. Arrows: Digits on arrows indicate the distance to the nearest cell of the same colour in the indicated direction (Adjacent cells are a distance of 1 from each other). Not all arrows are necessarily given.