Learn a deduction, then use it

Queens Line Lock: Row and Column Elimination

A line lock occurs when all candidates in one region occupy the same row or column. That line is reserved for the region’s Queen, so candidates outside the region can be eliminated. The same argument also works in the reverse direction.

Every figure below is a real, verified intermediate position. Dots are remaining candidates; × cells were excluded by earlier deductions. A white outline shows the deduction’s focus.

Three worked examples

Example 1

All remaining candidates in region 6 lie in column 7. Its Queen must occupy that group. Exclude the 2 outside candidates marked ×, because that group cannot contain a second Queen.

Position after 3 verified deductions on 7×7 puzzle #3.

Before the deduction. Rows run top to bottom; columns left to right. Numbers identify regions; × means excluded.
After the deduction. Rows run top to bottom; columns left to right. Numbers identify regions; × means excluded.
Play the complete original puzzle

Example 2

All remaining candidates in region 2 lie in row 2. Its Queen must occupy that group. Exclude the 2 outside candidates marked ×, because that group cannot contain a second Queen.

Position after 3 verified deductions on 7×7 puzzle #6.

Before the deduction. Rows run top to bottom; columns left to right. Numbers identify regions; × means excluded.
After the deduction. Rows run top to bottom; columns left to right. Numbers identify regions; × means excluded.
Play the complete original puzzle

Example 3

All remaining candidates in column 7 lie in region 5. Its Queen must occupy that group. Exclude the 1 outside candidates marked ×, because that group cannot contain a second Queen.

Position after 3 verified deductions on 7×7 puzzle #26.

Before the deduction. Rows run top to bottom; columns left to right. Numbers identify regions; × means excluded.
After the deduction. Rows run top to bottom; columns left to right. Numbers identify regions; × means excluded.
Play the complete original puzzle

A tempting mistake

Region 3 still has candidates in more than one column. It does not reserve column 4; a candidate in another column would break that claim.

Counterexample: no candidates have been eliminated. Rows run top to bottom; columns left to right. Numbers identify regions; × means excluded.

Try the deduction yourself

Every highlighted candidate in column 5 lies in region 3. Select one outside candidate that this lock eliminates. This position follows 4 verified deductions.

Technique exercise. Rows run top to bottom; columns left to right. Numbers identify regions; × means excluded.

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