Lesson 3 of 8
Locked candidates
Locked candidates are the first technique that removes candidates instead of placing digits. When every cell that can hold a digit inside a box sits in one row or column, the box must put that digit somewhere along that line, which rules it out of the rest of the line. Run it the other way round and it rules a digit out of the rest of a box.
- Level
- Intermediate
The pattern
What it does.
Pointing: inside a box, the cells that can still take a digit all share a single row or column. The box has to place the digit in one of them, so the digit can't appear anywhere else in that row or column outside the box.
Claiming: inside a row or a column, the cells that can still take a digit all sit inside one box. The line has to place the digit in that box, so the digit can't appear anywhere else in the box.
Neither form places anything. Both take candidates away, and the value is that the removal is often what uncovers a single candidate next.
Example
A worked example.
Take one digit in one box
Pick a box and a digit that isn't placed in it. Note every cell in the box that can still take that digit, by checking the rows and columns that cross the box.
See whether they share a line
If all of those cells sit in the same row, the digit is locked to that row within the box. The same goes for a column.
Eliminate along the line
Remove the digit from every other cell of that row or column, outside the box. The box still has to place it, so those cells can never hold it.
Then try it the other way round
For claiming, start inside a row or column instead: if every cell that can take the digit lies within one box, remove the digit from the rest of that box. Sweeping the whole grid both ways is what makes the technique pay.
Spotting it
How to spot it.
- Boxes where the possible cells for one digit line up along an edge, which usually means a neighbouring box has already taken the digit out of the rest of that line.
- Digits with only two or three possible cells left in a box. The fewer there are, the more likely they share a line.
- A candidate list that has stopped producing singles: a locked candidate is often what's missing.
Where it stops working
Locked candidates never place a digit directly, so a puzzle that needs them can look stuck for several moves before anything lands. The eliminations also depend on a complete candidate list: one digit missing from one cell is enough to make "all of them share a line" false, and the technique will then remove a candidate that was never impossible.
Keep going
Related topics.
New to sudoku? The rules take two minutes to read, and the first-puzzle walkthrough covers the basics that come before any of these.
Practice it in Sudoku Mori.
Locked candidates is lesson 3 in the game, with a worked example and three practice puzzles. Lesson puzzles are separate from your daily ones, and you can redo any lesson whenever you like.