Normal sudoku rules apply: Place the digits 1-9 once each in every row, column, and 3x3 box. Draw a 1 cell wide loop through the centers of some cells. The loop only moves orthogonally and cannot branch or touch itself, even diagonally. A digit in a circle on the loop indicates how many circles on the loop contain that digit. Similarly, a digit in a circle off the loop indicates how many circles off the loop contain that digit. Black dots separate digits where one is double the other. Additionally, exactly one cell touching a black dot is on the loop, and the other is off the loop. White dots separate consecutive digits. Additionally, the two cells touching a white dot are either both on the loop, or both off the loop. Not all dots are necessarily given.