Sudoku Triples

Outcome

You can recognize a three-cell / three-digit subset from either direction: Naked by counting the candidate union across cells, Hidden by counting the positions available to digits.

Intro copy

Pairs scale to Triples.

The logic is still:

N cells reserve N digits.

What gets harder is recognition.

This lesson teaches two different things to count.

Part 1 — Naked Triple: count digits across cells

Show:

• {2,5}
• {2,7}
• {5,7}

UI calculates:

Union = {2,5,7}

Prompt:

Three cells. How many distinct digits?

Correct: 3.

Reveal:

Those three digits are reserved for these three cells.

Learner removes 2/5/7 from other cells in the unit.

False example

Show:

• {2,5}
• {2,7}
• {5,8}

UI:

Union = {2,5,7,8}

Prompt:

Naked Triple?

Correct: No.

Feedback:

Three cells but four digits. The set is not restricted enough.

Part 2 — Guided Naked Triple

No identical candidate sets.

Learner:

1. selects three small candidate cells;
2. sees union visualization;
3. verifies 3 cells / 3 digits;
4. removes subset digits elsewhere.

Correct feedback:

Good. Naked Triples are about the candidate union, not three matching cells.

Part 3 — Hidden Triple: count positions across digits

Switch the interaction.

Highlight three candidate digits one at a time.

Their combined positions fit entirely inside three cells.

Prompt:

Three digits. How many cells contain all of their possible positions?

Correct: 3.

Reveal:

Those cells are reserved for the three digits.

Learner removes every non-target candidate from the three cells.

Part 4 — Guided Hidden Triple

Target cells contain extra notes.

Learner must:

1. choose three restricted digits;
2. compare their position maps;
3. identify the three-cell set;
4. clean the cells.

Incorrect feedback:

Do not compare the candidate counts inside the cells. Track where the target digits can appear across the whole unit.

Part 5 — Naked vs Hidden

Show both states side by side.

Prompt:

Where does the elimination happen?

Naked

Remove subset digits from outside the three cells.

Hidden

Remove non-subset digits from inside the three cells.

Then show the unifying statement:

Both techniques prove the same 3-digits / 3-cells reservation from opposite directions.

Practice

Six controlled states:

1. obvious Naked Triple;
2. non-identical Naked Triple;
3. false Naked Triple with four-digit union;
4. Hidden Triple in row;
5. Hidden Triple in box;
6. Naked-vs-Hidden classification.

Hint ladder — Naked

1. “Look at small candidate sets.”
2. “Select three cells in one unit.”
3. “Count the distinct candidates across them.”
4. “The union contains exactly three digits.”
5. Highlight outside eliminations.

Hint ladder — Hidden

1. “Follow digits, not cells.”
2. “Which digits each have only a few positions?”
3. “Their combined positions fit inside three cells.”
4. Highlight the three reserved cells.
5. Highlight extra candidates to remove.

Checkpoint

Present one Naked and one Hidden Triple without labels.

Prompt:

Solve both subsets and explain why the eliminations happen in different places.

Completion

• two Naked Triples;
• one false Naked Triple;
• two Hidden Triples;
• one correct Naked-vs-Hidden explanation.

Next

Intermediate Practice

Now remove the technique labels and decide which intermediate family the candidate structure suggests.

Reference

Read Naked Triple and Hidden Triple for the full rules, Locked Triple context, and recognition tips.