Fillomino: Divide the grid into polyominoes so that polyominoes of the same size don't share an edge. Each cell contains a number equal to its polyomino's size. Draw a loop that moves orthogonally from one cell to another through the grid. The loop must not touch itself orthogonally; however, it can touch diagonally. Along the loop, any three consecutive cells must contain numbers congruent to 0 mod 3, 1 mod 3, and 2 mod 3. (In other words, one of the numbers is from the set {3, 6, 9, 12, …}, one is from {1, 4, 7, 10, …}, and one from {2, 5, 8, 11, …}. Numbers on cells with arrows refer to the total amount of loop cells seen in the indicated direction or, if more than one arrow, in the directions combined.
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