KenKen Combinations

KenKen cage combinations are a whole different beast to those you may be used to with Killer Sudoku. That is because the Killer Convention does not apply. Cages can have duplicate numbers provided they do not duplicate in the rows and columns. If a cage is all in a line then the duplication doesn't arise. But if there is any kind of kink - what I call a "dog leg", then we have to include duplicates. But how many dog-legs can there be in a KenKen cage. Normal 6x6 KenKen has a cap of 6 cells in a cage although these are rare. Two cell cages must be adjacent and therefore can never have a dog-leg. So from three to six cells we need a combinations table for each of the number of dog-legs.

See the article on KenDoku Dog Legs for a distinction between the two types of puzzles.

The tables below are separated into three. These are the combinations for no dog-legs, one dog-leg and two. Beyond that the solver will compute the combinations on the fly.

I have created this diagram which shows all the possible cage shapes with the maximum number of duplicate positions. These are labelled A and B - since some cages we can have more than one duplicate solution number.