Break the grid entirely into "ominos" ie orthogonally-connected regions of some size. Each omino contains a digit equal to the size of its omino (in number of cells), and two ominos of the same size may not touch orthogonally (but may touch diagonally). Draw a loop that moves orthogonally through the centres of some cells. The loop must visit each omino exactly once, but may visit any number of cells within that omino from one up to the full size of the omino. If two orthogonally adjacent cells are both unvisited by the loop, there cannot be a border between them. The grid line pointed at by an arrow acts as a border between ominos. The number in the target cell (ie the cell the arrow points to) gives the number of cells within the omino containing the arrow that are visited by the loop.