KenKen Strategies

If two cells in the same row or column both have exactly the same two candidates (e.g., 5), then those two digits must go in those two cells. You can eliminate 2 and 5 from all other cells in that row or column.

How to spot them: Use pencil marks to track candidates. When two cells share the same pair, highlight them and eliminate those digits from the rest of the row/column.

Extended: The same logic applies to naked triples (three cells sharing three candidates) and naked quads. These are rarer but equally powerful.

A hidden single occurs when a digit can only go in one cell within a row or column, even though that cell might have multiple candidates. The digit is "hidden" among other possibilities.

How to find them: For each digit 1-N, scan each row and column. If a digit appears as a candidate in only one cell of that row/column, it must go there.

Why it works: Every digit must appear in every row and column. If there's only one possible cell for it, that's where it goes.

For each cage, list all possible digit combinations that produce the target. Then cross-reference with row/column constraints to narrow the possibilities.

Key insight: Some cages have surprisingly few valid combinations. In a 6×6 grid, 1− can be 2, 3, 4, 5, or 6 — but row/column constraints often eliminate most of these. Check our combination tables for quick reference.

Forced digits: If a digit appears in every valid combination for a cage, it must be in that cage. This is especially useful for multiplication and division cages.

When two or more cages share the same row or column, their digit requirements interact. The candidates in one cage restrict what's possible in adjacent cages.

Example: If a row has two 2-cell cages, and one cage requires 4 or 3, while the other requires 5 or 4, you can analyze which combinations leave valid options for the remaining cells.

Advanced technique: If all cells of a cage lie within a single row (or column), the cage's digits must be a subset of that row's digits. Use this to constrain both the cage and the remaining cells in the row.

The parity (odd/even nature) of a target can restrict which combinations are valid. Addition targets: an odd sum requires an odd number of odd digits. Multiplication targets: an even product means at least one digit must be even.

Subtraction: If the target is odd, one digit must be odd and the other even. If the target is even, both digits must have the same parity.

When it helps most: Parity analysis is especially useful in larger grids (7×7+) where the number of candidates makes direct analysis harder.

Every row and column in an N×N KenKen grid sums to 1+2+...+N = N(N+1)/2. For a 6×6 grid, that's 21. If you know the sum of all but one cell in a row, the remaining cell is determined.

Cage overlap: If a cage spans multiple rows but most of its cells are in one row, you can compute the contribution to that row and deduce the remaining digits.

Example: In a 6×6 grid (row sum = 21), if cages fully within a row account for a sum of 15, the remaining cells must sum to 6.