Locked candidates in sudoku: Box and line interactions
Learn locked candidates in sudoku with pointing and claiming examples, clear elimination boundaries and an exercise you can explain without guessing.
What locked candidates mean
Locked candidates in sudoku use the intersection between a 3 × 3 box and a row or column. You do not need to know the final cell for a digit. Instead, establish that every possible place for that digit within one unit lies in its intersection with another unit. The digit is reserved for the intersection and can be removed from the rest of the second unit. Several possibilities can remain open afterwards. The useful result is an elimination that remains true even when you cannot yet decide which cell within the intersection will contain the digit.
Start with complete information for one digit
Choose a digit and check that it has not already been placed in the unit you are examining. Find all its possible locations there. You do not need complete lists for the other eight digits to study this one, but you must check every cell in the relevant unit. With partial pencil marks, an absent mark is not an established exclusion. Here r2c3 means row 2, column 3, counting from the top and left. These examples describe local positions under stated conditions; they are not complete puzzles and make no claim of a unique full-grid solution.
Local example: Box to row
In box 1, 6 fits only at r2c1 or r2c3. Remove 6 from r2c5 and r2c8.
Candidates to keep: r2c1, r2c3Candidates to remove: r2c5, r2c8
A local deduction model. Only the relevant positions are shown; blank cells do not mean that other candidates are absent.
Local example: Row to box
In row 5, 4 fits only at r5c4 or r5c6. Remove 4 from r4c5 and r6c4.
Candidates to keep: r5c4, r5c6Candidates to remove: r4c5, r6c4
A local deduction model. Only the relevant positions are shown; blank cells do not mean that other candidates are absent.
Box to row: A pointing example
In the upper-left box, 6 has not been placed and its only possible positions are r2c1 and r2c3. Both belong to row 2. The box must therefore place its 6 somewhere in row 2, whichever of the two cells is eventually chosen. Remove candidate 6 from other cells in row 2 outside the box, such as r2c5 and r2c8. Keep the candidates at r2c1 and r2c3: They support the argument. This reasoning does not allow you to clear 6 from the whole of column 1 or column 3.
Check both possibilities without choosing one
If r2c1 becomes 6, no other position in row 2 can contain 6. If r2c3 becomes 6, the same conclusion follows. Those two cases cover every location allowed in the box, and both rule out r2c5 and r2c8. You have not guessed between two answers; you have found something they both imply. Now test the boundary: If 6 were also possible at r1c2, the box candidates would no longer be confined to row 2. That extra possibility breaks this particular argument, so the outside candidates in row 2 must remain unless another deduction excludes them.
Row to box: The claiming direction
You can also start with a line. Suppose row 5 is missing 4 and allows it only at r5c4 or r5c6. Both cells are in the centre box. Because row 5 must place its 4 inside that box, no other cell in the box can contain another 4. Remove the candidate from r4c5 and r6c4 if it is present there. Notice the direction: The row contains the complete starting set, and the remaining cells in the box receive the eliminations. You can use exactly the same reasoning with a column as your starting unit.
A practical search order
Inspect boxes first and group the positions of one digit by row and column. When every position falls on a single line, look for candidates outside the box along that line. Then reverse the search: Inspect lines and ask whether all their positions fall within one box. The intersection can contain two or three possibilities. The requirement is confinement, rather than a fixed count of two. Make one justified elimination at a time and remember the reason for it. After updating the affected notes, return to naked and hidden singles before spending time on more complicated patterns.
Exercise: Identify the affected cell
In the lower-left box, 8 can appear only at r7c2 or r8c2. Can you eliminate 8 from r3c2, r7c5 or r4c8? The answer is r3c2, which shares column 2 with both required positions and lies outside their box. The argument does not eliminate 8 from r7c5, because it is outside that column. It also leaves r4c8 unchanged, since that cell sees neither starting position. This exercise checks the reach of the pattern; it does not ask you to place 8 or finish a grid. Both cells in the intersection remain candidates.
Explain the boundary before deleting a mark
Name the digit, starting unit, intersection and affected unit before making an elimination. If you cannot explain why the target cell sees every position in the intersection, inspect the move again. Do not confuse two cells sharing one candidate among several notes with a naked pair; this technique follows one digit through two units. Practise recognition at a comfortable pace, then revisit basic techniques after each elimination. A grid will not necessarily offer a locked-candidate move at the particular moment you decide to search for one, so an unsuccessful search is a reason to change your focus.
Which cell allows a new elimination of 8 from this pattern?
Local example: In the lower-left box, 8 is possible only at r7c2 or r8c2.
Further reading
Now try it on the grid.
Practise at your own pace and look for a chance to explain the next deduction.
Practise with a Sudoku