Keen / KenKen
Can a number repeat inside a Keen cage?
Yes, if the repeated digits are not in the same row or column and the cage arithmetic is correct. Keen enforces uniqueness by row and column, not by cage. Killer Sudoku uses a different cage rule.
Worked example
In an L-shaped 4+ cage, values 1, 2, 1 can satisfy the sum if the two 1s are diagonally separated and the surrounding rows and columns permit them.
What to check on your board
Apply the rule above to your current board, then verify the remaining puzzle constraints. The example explains a local deduction; it is not a solution to every randomly generated board.
Checking your next move
List the combinations that satisfy the cage operation, then filter them against the rows and columns they occupy. Do not discard a repeated value merely because it occurs twice in a cage. Check the positions of those repetitions and the arithmetic separately.
Using this reference
For Keen / KenKen, read the rule and the worked example together before opening the game. Separate what the rule explicitly requires from what only seems likely on the current board. A useful next move is one you can explain from the visible constraints, not merely a pattern that looks familiar.
If you get stuck, isolate a smaller part of the position and list what is still possible there. After a move, check the affected rows, regions or connections again. The reference explains the documented rules; progress, controls and save behavior belong to the linked game.
Read the developer’s manual ↗ · Open the developer’s browser version ↗
Manual inspected: · Simon Tatham & contributors · MIT