KenKen Cage Combinations
Reference tables showing every valid digit combination for each cage size, operation, and target number. Select a grid size below.
- Digits
- 1–3
- Max cage size
- 3 cells
- Operations
- +, −, ×, ÷
- Digits
- 1–4
- Max cage size
- 4 cells
- Operations
- +, −, ×, ÷
- Digits
- 1–5
- Max cage size
- 4 cells
- Operations
- +, −, ×, ÷
- Digits
- 1–6
- Max cage size
- 4 cells
- Operations
- +, −, ×, ÷
- Digits
- 1–7
- Max cage size
- 4 cells
- Operations
- +, −, ×, ÷
- Digits
- 1–8
- Max cage size
- 4 cells
- Operations
- +, −, ×, ÷
- Digits
- 1–9
- Max cage size
- 4 cells
- Operations
- +, −, ×, ÷
What are Cage Combinations?
In KenKen puzzles, cells are grouped into cages — outlined regions with a target number and an arithmetic operation. The digits placed in the cage's cells must produce the target value when combined using the specified operation.
Knowing all possible digit combinations for a given cage is a fundamental solving technique. For example, in a 6×6 grid, a 2-cell cage with "11+" can only contain 6 — there's only one combination. Identifying forced combinations helps narrow down candidates quickly.
These reference tables list every valid combination for each grid size. Use them while solving or as study material to improve your speed. See our strategies guide for how to apply cage analysis effectively.