Practise: Cage-Line Reduction
This trainer opens at the verified Cage-Line position. The marked 22-cage already guarantees 9, while the blue cell still shows 9 as a normal row candidate.
Ask whether 9 can remain in the blue cell. First find the digit shared by every combination of the marked 22-cage. Then see where 9 can still fit inside that cage: both positions are in the same row, so use the hint to confirm the elimination.
Your turn first
Spot the idea before the hint explains it
- 1. Look
- 2. Check
- 3. Proof
Look at the marked starting cell, cage outline and sum. Which digit or combination is forced, and what visible sum fact supports your idea?
How to spot it
Look for a cage with several remaining combinations that all share one digit. Next, inspect where that shared digit can still go inside the cage. The pattern appears only when those possible cage cells all share one row, column or box.
Put it to use
Where you will meet it
Expert grids are the only place this pattern regularly decides the solve. Bring your notes.
Play ExpertStuck on a grid of your own?
Type the position into the solver and it walks the whole solution, naming the technique behind every step — including this one.
Open the solver