Normal sudoku rules apply. In the grid is a “galaxy” ie an orthogonally-connected group of cells centred on the middle cell of the grid and rotationally symmetric by 180° around that cell. Eg if r3c3 was in the galaxy then r7c7 must also be in the galaxy. The galaxy contains ALL of the cells containing odd digits but none of the cells containing even digits. Digits do not repeat in a cage and sum to the total given in the top left corner of the cage. Cells separated by an X contain digits summing to 10. The grid is covered in fog. Placing correct digits will clear the fog from the surrounding cells. No guessing is necessary.