Place the digits 0 to 9 once into each row, column, and 3x3 box. One cell in each row, column, and box is an S-cell containing two digits. The value of an S-cell is the sum of its digits; no two S-cells contain the same pair of digits. Fog covers some cells, and will be cleared when a correct single digit is placed in a cell; S-cells do not clear fog. “Renban loops” contain a set of consecutive values in any order. Each loop is a different colour of thick line, and does not cross or intersect itself. The value in a circle is equal to the sum of the values along the attached arrow. Each arrow is a different colour of thin line, and does not branch. The values in cells surrounding an X sum to 10, and the values in cells surrounding a V sum to 5. A cell with a grey square contains an even value.