Normal sudoku rules apply. Draw a one-cell-wide loop of orthogonally connected cells. The loop may not touch itself, not even diagonally. The loop acts as an entropic line. Each set of three adjacent digits along the loop must be one low [123], one medium [456], and one high digit [789]. The loop must enter every cell of every cage. The sum of all digits in any given cage is the same for every cage (that sum must be determined by the solver).