Subsets & Locked Candidates

Locked Candidates — Pointing & Claiming

Locked Candidates removes a digit from cells without placing anything. If every place for a digit inside a box lies on one row or column, the digit must land on that short stretch, so it leaves the rest of the line — that is pointing. If every place for a digit in a row or column lies inside one box, it leaves the rest of that box — that is claiming, and both forms often open a Hidden Single nearby.

What you need to see on the grid

Reach for Locked Candidates as soon as naked and hidden singles stop coming. Work one digit at a time and look where boxes meet rows and columns. Four terms carry the whole method:

The intersection: A box shares exactly three cells with each row that crosses it, and three with each column. Both forms are about one of these three-cell stretches: the digit is shown to be somewhere inside it, even though you do not know which of its cells holds it.
Pointing: Start from a box. If all the cells of the box that still accept the digit lie on one row (or column), the box "points" along that line: the digit is removed from the line's six cells outside the box.
Claiming (box-line reduction): Start from a row or column instead. If all its cells that still accept the digit lie in one box, the line "claims" the digit for its stretch of that box: the digit is removed from the box's six cells off the line.
Locked candidate: A candidate confined to an intersection is locked there. The cells of the intersection keep it; only the cells beyond it lose it. The move never tells you which cell holds the digit, so it never places a number by itself.

How to apply it, step by step

One example runs through all four steps: the digit 7, on a position built so that both forms happen on the same board. Every diagram shows the whole grid. The cells a step needs are filled in; the others are left blank and hatched, so you know you can ignore them.

Step 1Pick a digit and a box, and find where it can go

Choose a digit the box is still missing and list every cell of the box that can take it. Box 8 has no 7 yet. Its five filled cells are out, and R7C5 and R9C5 are out too, because column 5 already has its 7 at R6C5. That leaves two places: R7C4 and R7C6.

Two or three places is what you are hoping for. A single place would be a Hidden Single — just play it. Four or more cannot all sit on one line.

Box 8 and the 7 at R6C5, which rules column 5 out. 7 can go only in R7C4 and R7C6.
	C1	C2	C3	C4	C5	C6	C7	C8	C9
R1
R2
R3
R4
R5
R6					7
R7
R8				2	5	3
R9				8		6

Digit already on the grid
Box 8, the box being read
A place for 7 in box 8
Candidate 7, the digit studied
Not needed for this step

Filled in: box 8; cell R6C5. The other 71 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.

Step 2Places on one row: point along it (pointing)

R7C4 and R7C6 are both on row 7. Box 8 needs a 7, and it can only go in one of them — so the 7 of box 8 sits on row 7, inside the box. Row 7 holds 7 only once, which means none of its cells outside box 8 can take it.

Remove 7 from every cell of row 7 outside the box that lists it: R7C2, R7C3 and R7C7. Leave the cells inside the box alone — those are where the 7 is locked. The same works for a column: if the places lined up in one column, you would clear that column instead.

Technique: Locked Candidates (pointing/claiming)

Box 8 and row 7 in full. The 7 of box 8 is locked to R7C4 or R7C6, so 7 leaves R7C2, R7C3 and R7C7.
	C1	C2	C3	C4	C5	C6	C7	C8	C9
R1
R2
R3
R4
R5
R6					7
R7	5							2	6
R8				2	5	3
R9				8		6

Digit already on the grid
Box 8, the box being read
Row 7, the line box 8 points along
A place for 7 in box 8
Candidate 7, the digit studied
Candidate removed
Not needed for this step

Filled in: row 7; box 8; cell R6C5. The other 65 cells are left blank: they are not needed for this step. Removed: 7 from R7C2, R7C3 and R7C7.

Step 3Places in one box: clear the rest of it (claiming)

Now turn the question around and start from a line. Row 2 has only two empty cells, R2C1 and R2C3, and both list 7 — so its 7 must be in one of them. Both sit in box 1. Whichever it is, box 1 gets its 7 on row 2, so no other cell of box 1 can take 7.

Remove 7 from the box's cells off row 2 that list it: R1C2 and R3C3. Here the two cells hold only 4 and 7, so a Naked Pair would reach the same result — but claiming works even when the cells carry other digits as well, and it only asks about one digit.

Technique: Locked Candidates (pointing/claiming)

Row 2 and box 1 in full. Row 2 keeps 7 inside box 1, so 7 leaves R1C2 and R3C3.
	C1	C2	C3	C4	C5	C6	C7	C8	C9
R1	9		1
R2		5		9	8	2	6	1	3
R3	6	8
R4
R5
R6
R7
R8
R9

Digit already on the grid
Row 2, the line being read
Box 1, the box row 2 claims 7 in
A place for 7 in row 2
Candidate 7, the digit studied
Candidate removed
Not needed for this step

Filled in: row 2; box 1. The other 66 cells are left blank: they are not needed for this step. Removed: 7 from R1C2 and R3C3.

Step 4Collect what the eliminations unlock

Locked Candidates never places a digit itself, so look at the units that just lost candidates. Column 2 had three places for 7: R1C2, R5C2 and R7C2 (R6C2 is ruled out by the 7 at R6C5). Claiming took R1C2 and pointing took R7C2. R5C2 is the only cell left for 7 in the column: a Hidden Single.

Neither form alone was enough — it took both. Check every row, column and box that lost a candidate before you move on.

Technique: Hidden Single

Column 2 after both eliminations, and the 7 at R6C5. 7 now fits only R5C2.
	C1	C2	C3	C4	C5	C6	C7	C8	C9
R1
R2		5
R3		8
R4		9
R5		7
R6					7
R7
R8		6
R9		1

Digit already on the grid
Column 2: one place left for 7
The cell that must be 7
Candidate 7, the digit studied
Digit placed
Not needed for this step

Filled in: column 2; cell R6C5. The other 71 cells are left blank: they are not needed for this step. Placed: R5C2 = 7.

Common mistakes

Missing a place elsewhere in the box

Pointing needs every place for the digit in the box to sit on the line — not most of them. One forgotten candidate on another row of the box, or a pencil mark you never wrote in, breaks the proof. Count all of the box's cells for that digit before you erase anything, as in step 1.

Clearing the wrong side of the intersection

Pointing clears the line outside the box; claiming clears the box outside the line. Erase the digit from the intersection itself and you have deleted the very cells where it is locked — in the example, removing 7 from R7C4 or R7C6 would leave box 8 with no place for 7 at all.

Writing a digit straight from the pattern

Locked Candidates tells you which line or box the digit is on, never which cell. Box 8 still has two places for 7 after step 2. If you catch yourself filling in a number from the pattern, stop and look for the single the eliminations create somewhere else, like R5C2 in step 4.

Recent daily puzzles that needed this technique

Learn the move, not just the digit

In a real game, when Locked Candidates is what opens the next cell, the hint in the app names it and, for each cell it rules out, says which box or line has the digit locked — the reasoning of steps 2 to 4 above.

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