How to Solve a 4x4 Killer Sudoku
Keep the four digits 1, 2, 3 and 4 in mind and look for the cages that allow only one combination: a two-cell cage of sum 3 is 1 and 2, one of sum 7 is 3 and 4, and a three-cell cage of sum 9 is 2, 3 and 4. A single-cell cage simply gives its digit. Then use the rule of ten: every row, every column and every 2x2 box adds up to 10, so when a cage fills a row but for one cell, that cell is 10 minus the cage sum.
Place a digit, cross it off in its row, its column and its box, and move to the cage that just became forced. In a 4x4 grid, two or three such steps usually unlock the whole puzzle, with no guessing at any point.