CHAOS CONSTRUCTION: Divide the grid into 8 regions each containing 8 orthogonally connected cells, and fill the grid with the digits 1-8 so that digits don't repeat in a row, column or region. DOUBLERS: Each row, column and region contains exactly one doubler cell. The value of a doubler cell is double its digit. Each doubler cell contains a different digit. QUADSWALLOP: Each digit 1-8 is represented by a different letter of the alphabet, to be determined. In each grey quad circle, 4 of the letters correspond to the digits (not values) in the surrounding 4 cells, but there is also one lying letter which does not correspond to any of the surrounding digits. The purple and green circles on the right can be used to keep track of letters in the grid, and their corresponding digits. PURPLE X: Values separated by a small purple X sum to 10, and are in the same region. The two ends of a grey, red or blue line always lie in different regions. Red and blue lines have an additional rule: PARITY LINES (RED): Two adjacent cells along a red line contain one even value and one odd value. REGION SUM LINES (BLUE): Region borders divide blue lines into segments which each have the same total value.