Tentative Looping

• Normal sudoku rules apply, i.e. each row, column, and 3x3 region has to contain the digits from 1 to 9 once each.

• Tenline Loop: Draw a one-cell wide loop into the puzzle. The loop may only move orthogonally from cell to cell and must not touch itself neither orthogonally nor diagonally. Moreover, the loop acts as a tenline, i.e. it can be split into contiguous, non-overlapping segments that sum to exactly 10.

• Loop sum clues: Clues outside the grid indicate the sum of all digits ON THE LOOP in the respective row or column. (Digits that are not on the loop do not contribute to the sum.)

• Connecting Kropki: Cells joined by a white dot must contain consecutive digits. Moreover, exactly one of the cells is on the loop and the other is not.

Cells joined by a black dot must contain digits with a 1:2 ratio. Moreover, either both cells lie on the loop or they both do not. (Not all dots are given.)