Normal sudoku rules apply. The circles given in the grid are the centers of pointsymmetric "galaxies", which function as cages for the Killer Sudoku. The numbers inside the circles indicate the sum of the digits in the cages. In addition, each cage is a "thermometer". Along thermometers, digits must increase from the bulb end, but the bulb end is not given. The cages/thermometers cannnot "branch". Thermometers are also symmetrical about their circles. The digits in a cage/thermometer may not repeat. Not every cell in the grid has to be part of a galaxy.