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Mid-Loop
Normal Sudoku rules apply: Fill the grid with digits 1 to 9 appearing once each in every row, column, and 3x3 box.
Mid-Loop: Draw a single 1-cell-wide loop of orthogonally connected cells into the grid that enters no cell more than once. The loop must pass through all dots. All dots must be in the middle of a straight loop segment, i.e., the distance from a dot to the next turn along the loop must be identical in both directions. The loop acts as an Entropic Line. Any group of three consecutive cells along the loop must contain one low digit (1,2,3), one middle digit (4,5,6), and one high digit (7,8,9).
Kropki dots: Cells connected by a white dot contain consecutive digits. Digits in cells connected by a black dot are in a 1:2 ratio.
Mid-Loop: Draw a single 1-cell-wide loop of orthogonally connected cells into the grid that enters no cell more than once. The loop must pass through all dots. All dots must be in the middle of a straight loop segment, i.e., the distance from a dot to the next turn along the loop must be identical in both directions. The loop acts as an Entropic Line. Any group of three consecutive cells along the loop must contain one low digit (1,2,3), one middle digit (4,5,6), and one high digit (7,8,9).
Kropki dots: Cells connected by a white dot contain consecutive digits. Digits in cells connected by a black dot are in a 1:2 ratio.