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Module 4 · IntermediateLesson 14 of 28

Box-Line Reduction

Find a digit confined to one box within a row or column and eliminate that digit from the rest of the box.

Outcome

You can start from a row or column, recognize when all positions for one digit fall inside a single box, and remove that digit from the rest of the box.

Intro copy

Claiming is Pointing in reverse.

Pointing asks:

Does this box's digit live on one line?

Claiming asks:

Does this line's digit live inside one box?

Step 1 — Flip the arrow

Display:

Box → line = Pointing

Then reverse:

Line → box = Claiming

Use the same candidate geometry so only the source unit changes.

Prompt:

Which unit gives us the restriction this time?

Learner selects row/column.

Step 2 — Guided row Claiming

Required state: Row 6 has all candidate 2s inside box 5; the box contains other candidate 2s.

Prompt sequence:

  1. select every 2 in row 6;
  2. identify the one box containing all of them;
  3. remove 2 from that box outside row 6.

Correct feedback:

Good. Row 6 must place its 2 inside this box, so the rest of the box cannot contain 2.

Step 3 — Guided column Claiming

Same interaction vertically.

Incorrect feedback if learner eliminates from the column:

Keep the source candidates. Claiming removes from the box outside the source line.

Step 4 — Three source positions

Use all three cells of a row/box intersection as possible 6s.

Prompt:

Does Claiming need exactly two source cells?

Correct: No.

Feedback:

The row still places 6 somewhere inside this box. Two or three source positions can support the same deduction.

Step 5 — Compare Pointing vs Claiming

Show two patterns side by side.

Pattern A:

  • box restricts digit to row.

Pattern B:

  • row restricts digit to box.

Prompt:

Which is Claiming?

Then:

Where does each pattern eliminate?

The goal is to classify by source direction, not by shape.

Practice

Five states:

  • row Claiming;
  • column Claiming;
  • three-source form;
  • Pointing-vs-Claiming comparison;
  • near-miss where another source candidate exists in a second box.

Hint ladder

  1. “Follow one digit across the highlighted row/column.”
  2. “How many boxes contain its candidate positions?”
  3. “All positions are inside one box.”
  4. “The line has claimed the digit for that box.”
  5. Highlight the outside-box eliminations.

Completion

Four Claiming eliminations plus one correct Pointing/Claiming comparison and one near-miss rejection.

Next

Naked Pairs

Intersections reserve one digit for a region. Subsets reserve multiple digits for multiple cells.

Reference

Read Box-Line Reduction for the full Claiming proof and naming.