X-Wing

Outcome

You can find a size-2 Fish for one digit, identify base and cover units, reject a false rectangle, and eliminate the digit from valid cover-set targets.

Intro copy

Do not memorize an X-shaped picture.

Learn one rule:

Two source units require two placements, and all source positions fit inside two cover units.

That is X-Wing.

Step 1 — Build base and cover sets

Filter candidate 5.

Show:

r2 → c4/c8
r7 → c4/c8

Prompt:

Which units require the two 5 placements?

Learner selects rows 2 and 7.

Label:

Base sets

Prompt:

Which units cover every possible source position?

Learner selects columns 4 and 8.

Label:

Cover sets

Then reveal outside candidate 5s in c4/c8.

Prompt:

Which candidates can the base rows no longer allow?

Learner removes them.

Step 2 — Two possible diagonals

Animate:

Case A

• r2c4 = 5;
• r7c8 = 5.

Case B

• r2c8 = 5;
• r7c4 = 5.

Prompt:

What stays true in both cases?

Expected:

Columns 4 and 8 receive their 5s from the two base rows.

This teaches the proof before the label.

Step 3 — Guided row X-Wing

Learner:

1. chooses target digit;
2. finds first two-position row;
3. finds matching row;
4. labels base/cover units;
5. eliminates outside cover candidates.

Correct feedback:

Good. The two rows consume the two cover columns.

Step 4 — Column X-Wing

Transpose the pattern.

Prompt:

What changed?

Correct:

Columns are now the base sets and rows are the covers. The proof is unchanged.

Step 5 — False rectangle

Show four apparent corner candidates plus a third source candidate in one base row.

Prompt:

X-Wing?

Correct: No.

Feedback:

The rectangle is visual noise. One base row still has another legal position, so the two-cover restriction is not proven.

Step 6 — Valid but unproductive Fish

Show a valid X-Wing with no candidate to eliminate from either cover unit.

Prompt:

Is the X-Wing valid?

Yes.

Is it a useful move right now?

No.

This distinction prevents the learner from equating pattern existence with solving progress.

Practice

Progression:

1. target digit preselected;
2. one base unit hinted;
3. only candidate filter available;
4. no pre-highlighting;
5. false rectangle;
6. valid but unproductive X-Wing.

Hint ladder

1. “Follow one digit.”
2. “Find a row/column with exactly two positions.”
3. “Look for another source unit using the same two covers.”
4. “These are your base and cover sets.”
5. Highlight valid eliminations.

Completion

• two row-based X-Wings;
• two column-based X-Wings;
• one false rectangle rejected;
• one valid-but-unproductive Fish classified correctly.

Next

Swordfish

Keep the same proof and increase the set size from 2/2 to 3/3.

Reference

Read X-Wing for the full Fish proof, rectangle counterexample, and search routine.