Here are some advanced techiniques that can be used for helping to solve KenKens. They are written for 6x6 puzzles, but similar principles can be applied to all sizes.
1. Every row and every column adds up to 21. This can be applied to a single row/column or multiple rows/columns.
2. Every row and every column has three odd numbers and three even numbers.
3. Every odd difference or two-box sum that is an odd number must contain one even number and one odd number.
4. Every difference of 2 must contain a 3 or a 4. So, for example, if a row contains both a 2- and a 7+, the 7+ cannot be 3+4.
5. If two 2x2 rectangles are directly aligned with one another, they can't both contain the same pair of numbers. For example, if a 5- in one row is directly aligned with a 7+ in another row, the 7+ cannot be 1+6. The reason is that if there were a valid solution in which this is the case, you could interchange both pairs of numbers and have another valid solution. And since each KenKen puzzle has a unique solution, the correct solution cannot have this feature.
