Normal sudoku rules apply. Digits along the gray lines must have values in between the values of the digits in the attached circles. (There is a line connecting the circles in r1c1 and r1c4, and a separate line connecting the circles in r1c4 and r4c4. Also there is a line connecting the circles in r1c6 and r1c9, and a separate line connecting the circles in r1c9 and r4c9). The sum of the digits along each red line is equal to the sum of the digits in the attached circles. Cells separated by a V sum to five.