Skip to content
Sudoku Slate

Learn Sudoku

Locked candidates

One intersection. Two directions of reasoning.

Sometimes a digit has several possible cells, yet all of them share something useful: one row or column inside a box. You cannot place the digit yet. You can still prove where it cannot go.

When to use it

Pointing starts in a box: if every remaining position for a digit in that box lies on one row or column, remove the digit from that line outside the box. Claiming starts in a line: if all its positions for a digit lie inside one box, remove the digit from the rest of that box.

How to find it

  1. 01

    Choose one digit and inspect every remaining position in the source unit.

  2. 02

    Confirm that all those positions belong to the same box-line intersection.

  3. 03

    Remove the digit only from the target unit outside that intersection.

Pointing: start inside the box

v1-hard-0001 · position before step 12

Sudoku position with the recorded logical candidatesRows and columns are numbered 1 to 9. Find the pattern before revealing the supporting cells. A complete text table follows the diagram.c1r1c2r2c3r3c4r4c5r5c6r6c7r7c8r8c9r9
Small digits are the candidates at this exact step, including earlier logical eliminations. No answer is filled in for you.
Read the position as a cell table
Each cell’s placed digit or complete remaining candidate list.
CellValue / candidates
r1c1Placed: 2
r1c2Placed: 7
r1c3Placed: 3
r1c4Placed: 1
r1c5Placed: 8
r1c6Placed: 5
r1c7Placed: 4
r1c8{6, 9}
r1c9{6, 9}
r2c1Placed: 5
r2c2{1, 8, 9}
r2c3{4, 6, 8, 9}
r2c4{4, 6, 7}
r2c5{4, 6, 7}
r2c6{4, 6, 7}
r2c7Placed: 3
r2c8Placed: 2
r2c9{1, 6, 8, 9}
r3c1{1, 4, 8}
r3c2{1, 8}
r3c3{4, 6, 8}
r3c4Placed: 3
r3c5Placed: 9
r3c6Placed: 2
r3c7Placed: 5
r3c8{1, 6, 8}
r3c9Placed: 7
r4c1Placed: 3
r4c2{2, 5, 8, 9}
r4c3{2, 4, 5, 8, 9}
r4c4{4, 5, 8, 9}
r4c5{2, 4}
r4c6Placed: 1
r4c7Placed: 6
r4c8Placed: 7
r4c9{2, 4}
r5c1Placed: 7
r5c2{2, 5, 8}
r5c3{2, 4, 5, 8}
r5c4{4, 5, 6, 8}
r5c5{2, 3, 4, 6}
r5c6{4, 6, 8}
r5c7Placed: 9
r5c8{1, 4}
r5c9{1, 2, 3, 4}
r6c1{4, 9}
r6c2Placed: 6
r6c3Placed: 1
r6c4{4, 7, 9}
r6c5{2, 3, 4, 7}
r6c6{4, 7, 9}
r6c7Placed: 8
r6c8Placed: 5
r6c9{2, 3, 4}
r7c1Placed: 6
r7c2{1, 2, 5, 8, 9}
r7c3{2, 5, 8, 9}
r7c4{4, 7, 8, 9}
r7c5{1, 4, 7}
r7c6{4, 7, 8, 9}
r7c7{2, 7}
r7c8Placed: 3
r7c9{2, 4, 8, 9}
r8c1{1, 8, 9}
r8c2Placed: 4
r8c3{2, 8, 9}
r8c4{6, 7, 8, 9}
r8c5{1, 6, 7}
r8c6Placed: 3
r8c7{2, 7}
r8c8{6, 8, 9}
r8c9Placed: 5
r9c1{8, 9}
r9c2Placed: 3
r9c3Placed: 7
r9c4Placed: 2
r9c5Placed: 5
r9c6{4, 6, 8, 9}
r9c7Placed: 1
r9c8{4, 6, 8, 9}
r9c9{4, 6, 8, 9}

Look first. Reveal one layer at a time.

Find the supporting cells, explain the restriction, then inspect the candidates it removes. The original puzzle link starts from its givens; this panel preserves the intermediate logical state.

Play the original puzzle from its givens

Claiming: start in the line

Reverse the source and target units. All positions for one digit in the line lie in a single box, so the other cells of that box cannot use that digit.

v1-hard-0007 · position before step 16

Sudoku position with the recorded logical candidatesRows and columns are numbered 1 to 9. Find the pattern before revealing the supporting cells. A complete text table follows the diagram.c1r1c2r2c3r3c4r4c5r5c6r6c7r7c8r8c9r9
Small digits are the candidates at this exact step, including earlier logical eliminations. No answer is filled in for you.
Read the position as a cell table
Each cell’s placed digit or complete remaining candidate list.
CellValue / candidates
r1c1Placed: 7
r1c2Placed: 1
r1c3{2, 3, 4, 8}
r1c4{2, 9}
r1c5{2, 3, 9}
r1c6{2, 4}
r1c7Placed: 5
r1c8Placed: 6
r1c9{3, 8}
r2c1{2, 4, 5}
r2c2{2, 4, 5, 6}
r2c3{2, 3, 4, 5, 6}
r2c4Placed: 8
r2c5{2, 3, 5, 6, 7}
r2c6{2, 4, 6}
r2c7Placed: 1
r2c8{2, 7}
r2c9Placed: 9
r3c1Placed: 9
r3c2{2, 5, 6, 8}
r3c3{2, 3, 5, 6, 8}
r3c4{2, 5, 6, 7}
r3c5Placed: 1
r3c6{2, 6}
r3c7Placed: 4
r3c8{2, 7}
r3c9{3, 8}
r4c1{2, 4, 5}
r4c2Placed: 7
r4c3{2, 4, 5}
r4c4Placed: 3
r4c5{2, 5}
r4c6Placed: 8
r4c7Placed: 9
r4c8Placed: 1
r4c9Placed: 6
r5c1Placed: 8
r5c2{2, 6, 9}
r5c3{2, 6, 9}
r5c4Placed: 4
r5c5{2, 7}
r5c6Placed: 1
r5c7{2, 7}
r5c8Placed: 3
r5c9Placed: 5
r6c1{2, 5}
r6c2Placed: 3
r6c3Placed: 1
r6c4{2, 5, 6, 7}
r6c5{2, 5, 6, 7}
r6c6Placed: 9
r6c7{2, 7}
r6c8Placed: 8
r6c9Placed: 4
r7c1Placed: 3
r7c2{2, 4, 5}
r7c3{2, 4, 5}
r7c4{1, 2, 6}
r7c5{2, 4, 6}
r7c6Placed: 7
r7c7Placed: 8
r7c8Placed: 9
r7c9{1, 2}
r8c1Placed: 6
r8c2{2, 9}
r8c3{2, 7, 9}
r8c4{1, 2, 9}
r8c5Placed: 8
r8c6Placed: 5
r8c7Placed: 3
r8c8Placed: 4
r8c9{1, 2, 7}
r9c1Placed: 1
r9c2{2, 4, 8, 9}
r9c3{2, 4, 7, 8, 9}
r9c4{2, 9}
r9c5{2, 4, 9}
r9c6Placed: 3
r9c7Placed: 6
r9c8Placed: 5
r9c9{2, 7}

Look first. Reveal one layer at a time.

Find the supporting cells, explain the restriction, then inspect the candidates it removes. The original puzzle link starts from its givens; this panel preserves the intermediate logical state.

Play the original puzzle from its givens

When the rule does not apply

Suppose 7 is possible at r1c1 and r1c3 in the top-left box. They appear to point along row 1. But if r2c2 also permits 7, the digit could go there instead. You cannot remove 7 from the rest of row 1 on that evidence.

In that counterexample, is it valid to remove 7 from r1c5?

Show why

No. The extra candidate at r2c2 breaks the confinement to row 1. Two aligned candidates are not enough: all positions for that digit in the source box must align.

Try another position

This comes from a different puzzle. Use the condition, rather than the location you remember from the first example.

v1-hard-0002 · position before step 23

Sudoku position with the recorded logical candidatesRows and columns are numbered 1 to 9. Find the pattern before revealing the supporting cells. A complete text table follows the diagram.c1r1c2r2c3r3c4r4c5r5c6r6c7r7c8r8c9r9
Small digits are the candidates at this exact step, including earlier logical eliminations. No answer is filled in for you.
Read the position as a cell table
Each cell’s placed digit or complete remaining candidate list.
CellValue / candidates
r1c1Placed: 7
r1c2Placed: 1
r1c3Placed: 5
r1c4{2, 3, 6, 8}
r1c5{2, 3, 6}
r1c6{3, 8}
r1c7{4, 6, 8}
r1c8Placed: 9
r1c9{4, 8}
r2c1Placed: 9
r2c2{6, 8}
r2c3{6, 8}
r2c4Placed: 1
r2c5Placed: 4
r2c6Placed: 5
r2c7Placed: 3
r2c8Placed: 2
r2c9Placed: 7
r3c1{2, 3, 4}
r3c2{2, 3, 4, 6, 8}
r3c3{2, 3, 4, 6, 8}
r3c4Placed: 9
r3c5{2, 3, 6}
r3c6Placed: 7
r3c7{4, 6, 8}
r3c8Placed: 1
r3c9Placed: 5
r4c1Placed: 6
r4c2Placed: 9
r4c3{2, 3, 4}
r4c4{3, 4}
r4c5Placed: 5
r4c6Placed: 1
r4c7{4, 8}
r4c8Placed: 7
r4c9{2, 4, 8}
r5c1{1, 4}
r5c2Placed: 5
r5c3{1, 4}
r5c4Placed: 7
r5c5Placed: 8
r5c6Placed: 2
r5c7Placed: 9
r5c8Placed: 3
r5c9Placed: 6
r6c1Placed: 8
r6c2Placed: 7
r6c3{2, 3, 4}
r6c4{3, 4}
r6c5Placed: 9
r6c6Placed: 6
r6c7Placed: 1
r6c8Placed: 5
r6c9{2, 4}
r7c1{1, 2, 3, 4}
r7c2{2, 3, 4, 6, 8}
r7c3Placed: 7
r7c4{2, 3, 4, 6, 8}
r7c5{1, 2, 3, 6}
r7c6{3, 4, 8}
r7c7Placed: 5
r7c8{4, 6}
r7c9Placed: 9
r8c1{3, 4}
r8c2{3, 4, 6, 8}
r8c3Placed: 9
r8c4Placed: 5
r8c5Placed: 7
r8c6{3, 4, 8}
r8c7Placed: 2
r8c8{4, 6}
r8c9Placed: 1
r9c1Placed: 5
r9c2{2, 4, 6}
r9c3{1, 2, 4, 6}
r9c4{2, 4, 6}
r9c5{1, 2, 6}
r9c6Placed: 9
r9c7Placed: 7
r9c8Placed: 8
r9c9Placed: 3

A new position. Your deduction.

Which action is justified by this pattern? Inspect the full candidate state before choosing. You can ask for a hint at any time.

Choose the justified action

Play the original puzzle from its givens

Make the distinction

A pointing pair is not a naked pair. Pointing follows one digit across two or three cells. A naked pair reserves two digits for exactly two cells in one unit.

Compare with naked pairs

Related research