Hundreds of variations of Sudoku puzzles exist (see Pegg [2005] for a few examples). All Sudoku variations use deductive and spatial reasoning in finding solutions, but some draw on and support other mathematics. For example, Killer Sudoku puzzles require solvers to use basic addition and subtraction facts to find solutions. In these puzzles, solvers are given the sums of the distinctly different numbers that lie in a region bounded by a dotted border. No starting numbers are typically placed in the Killer Sudoku grids (see fig. 2a).